Bill Veeck, the baseball impresario who once sent a midget to bat as a pinch-hitter for the St. Louis Browns, died yesterday in Chicago at the age of 71 after a 45-year career as one of the most creative and provocative promoters in sports.

His life had involved a series of medical battles since he lost part of his right leg during action with the Marines in the South Pacific during World War II, an injury that led to dozens of operations in later years. He also underwent surgery for the removal of a malignant lung tumor 15 months ago, after conceding that he had smoked three or four packs of cigarettes a day for years and suffered from emphysema.

Last Monday, complaining of shortness of breath, he entered the Illinois Masonic Medical Center. He died there of a heart attack at 2:55 A.M. yesterday.

To his fellow executives in the big leagues, Bill Veeck was a rebel who owned the Cleveland Indians, the St. Louis Browns and the Chicago White Sox (twice), and who pulled outrageous stunts to promote them. To the public, he was a creative genius and an original: a craggy dynamo of a man who limped on an artificial leg, spoke in a hoarse voice, dressed casually, without necktie or overcoat, and created excitement and controversy wherever he staged events and drew crowds. Tossed Tradition to the Wind

To himself, he was ''Old Will,'' who expressed his sense of the entrepreneur's art in his books, ''Veeck, As In Wreck,'' and ''The Hustler's Handbook.'' He was amused that his showmanship often alarmed his fellow club owners in baseball or the racing establishment when he ran the Suffolk Downs track near Boston. He was criticized and even ostracized, but to all his critics and doubters, he offered one basic thought: ''Tradition is the albatross around the neck of progress.''

In pursuit of that wisdom, he wooed the public with tricks, gifts and bargains. He gave orchids to the women, placed gift certificates beneath the stadium or race-track seats, sent circus clowns to the coaching lines and even held a ''Grandstand Manager's Day,'' during which the Browns' strategy for one game was dictated by people in the grandstand, who were asked to signify by applause when signs were hoisted asking ''Infield in?'' or ''Should we walk him?''

But his most memorable stunt came on Aug. 19, 1951, when he was running the Browns, a team of perennial losers that lost 102 games that season and finished 46 games behind the Yankees, the pennant winners. Used Midget as a Pinch-Hitter

At a suitably dramatic moment in a game against the Detroit Tigers, he sent in a suitably dramatic pinch-hitter: Eddie Gaedel, a theatrical midget who stood 3 feet 6 1/2 inches tall. Gaedel promptly walked on four (high) pitches and ended his career as suddenly as he had started it.

Bob Fishel, now executive vice president of the American League, was working as Mr. Veeck's deputy in those days in both Cleveland and St. Louis, and yesterday he remembered the short but spectacular career of Eddie Gaedel.

''It was Bill's idea,'' he said, ''but I actually signed Eddie to a contract for $100. After he went to bat, the president of the league, Will Harridge, ruled that midgets were not eligible to play. But we had already released him. But Eddie made all the big TV shows as a guest, and made something like $17,000 in fees for that one time at bat.''

But Bill Veeck proved to be no mere stuntman. After he bought the Cleveland Indians in 1946, they won the American League pennant and the World Series in 1948 and played before 2,620,627 fans, a major league record at the time. After he bought the Chicago White Sox in 1959, they promptly won the pennant and set a club record by drawing 1,644,468 customers.

''Veeck was born into baseball and belongs there,'' Red Smith once wrote. ''He is an independent thinker, imaginative, uninhibited, innovative. He is a promoter at heart but a baseball man at bottom.'' At His Dramatic Best

Al Lopez, who was the manager of the White Sox in 1959, remembered Mr. Veeck at his dramatic best in that season: ''He promised he'd eat crow at State and Lake if I would win the pennant with that team. The following year, he went out to State and Lake and ate crow - or pheasant, or something.''

Bill Veeck was born into a baseball family on Feb. 9, 1914. His father, Bill Veeck Sr., was a Chicago baseball writer who became president of the Cubs, and young Bill would roam around Wrigley Field running errands and checking the turnstiles.

He studied law at Loyola University in Chicago, and once wrote a letter to Kenesaw Mountain Landis, the commissioner of baseball, warning that the ''reserve clause'' in contracts was illegal and probably doomed. He suggested a solution: sign players to seven-year contracts, the way the Hollywood film studios were doing. Nothing happened, but 40 years later the ''reserve clause'' was ruled illegal and the era of the free agent opened with revolutionary changes in sports.

In 1941, he took his first plunge into professional baseball as head of a syndicate that bought the Milwaukee Brewers, then a minor league team in the American Association. He hired the effervescent Charley Grimm as manager, and the two began to stage stunts and shows that turned the Brewers into a profitable team.

But two years later, he joined the Marines and was sent to the South Pacific, where his right leg was struck one day by the recoil of an antiaircraft gun. The leg was lost, and he later endured dozens of operations to mend the damage.

Back home, he returned to baseball in style in 1946: He was only 32, but he headed a group that bought the Indians. The team finished sixth that season, but two years later won the pennant and the World Series before record crowds. That team included the outfielder Larry Doby, who had been signed the season before as the American League's first black player. Owners Blocked Move

Three years later, Mr. Veeck turned his talents toward St. Louis and bought the struggling Browns, and struggled with them for three years in a city dominated by the Cardinals. His fellow owners refused to let him move the team, forced him to sell and then quickly allowed the new owner to move the Browns to Baltimore.

It took Mr. Veeck until 1959 to wedge his way back into the big leagues, but he did it with a clatter. He headed a group of investors who bought the White Sox, and once more found instant success. The team couldn't hit, but it could pitch, and it won the pennant in his first season as the resident magician. But the next year, the White Sox dropped into third place. In 1961, seriously ill at the time, Mr. Veeck sold the club to his partners, Arthur and John Allyn, and more or less retired to a country estate in Easton on Maryland's Eastern Shore.

His immediate aim was to restore his health, but he said: ''Old Will will be back.'' And he did come back - but this time as the operator of Suffolk Downs, where his creative mind was as sharp as ever. He staged Joe Fan Day, stashed a prize-winning certificate under one chair in the grandstand and awarded the winner a 3-year-old filly.

''Altruism is not one of my great gifts,'' he said. ''The average racing fan is slightly over 50 years of age. If you don't create new fans, how do you insure future growth, or even future existence?''

But baseball remained his main interest. In 1970, he tried to buy the Baltimore Orioles, but was blocked. In 1975, when the White Sox were packing to move to Seattle, he put together a financial group, bought them and kept them in Chicago.

Mr. Veeck stayed with the club five years, then tried to sell it to Edward J. DeBartolo Sr. This time he was blocked by Bowie Kuhn, the commissioner of baseball, reportedly because Mr. DeBartolo owned race tracks and did not live in Chicago. Mr. Veeck argued and lost, then sold the team to Jerry Reinsdorf, a real estate executive, for $20 million. This time, he left baseball for good.

''I didn't like the American League owners when I came into the league,'' he said, ''and I don't like them going out of it. Of course, I'm sure the feeling is mutual.''

He is survived by his wife, Mary Frances, and their six children, and by two children from a previous marriage. Services will be held tomorrow at St. Thomas the Apostle Church in Chicago.

William Louis Veeck