Born Shirley Ann Roque in Burlington, Vermont, Muldowney grew up in Schenectady, New York, where she began street racing in the 1950s as a teenager. At 16 she married Jack Muldowney, who built her first dragster and served as her mechanic. She made her dragstrip debut at Fonda Speedway in 1958 and obtained her NHRA pro license in 1965.
She competed at the 1969 and 1970 U.S. Nationals in a twin-engined Top Gas dragster. As the Top Gas class declined in popularity, she transitioned to Funny Car, purchasing her first car from Connie Kalitta. She and Jack Muldowney divorced in 1972, but remained friends until his death in 2007.
Muldowney stepped up to Top Fuel in 1973 and secured her Top Fuel license — the first woman to do so — behind the wheel of Poncho Rendon's car. Don Garlits was one of the three signatories on her application, alongside Tommy Ivo and Connie Kalitta. Garlits later said of her: "She went against all odds. They didn't want her to race Top Fuel, the association, the racers, nobody…just Shirley."
From 1973 to 1977, Muldowney partnered with Kalitta in match races as the Bounty Hunter and Bounty Huntress team. Her first major win had come earlier, at the IHRA Southern Nationals in 1971.
In Columbus, Ohio, in 1976, Muldowney delivered a dominant Top Fuel performance — qualifying number-one, setting low elapsed time and top speed in every round, and winning the class outright. The following season, 1977, she won the NHRA Winston world points championship: the first woman to claim drag racing's premier title. She won the championship again in 1980, and a third time in 1982 — becoming the first person in any category to win three NHRA Top Fuel titles.
The NHRA opposition to her career was considerable. Muldowney noted that "NHRA fought me every inch of the way, but when they saw how a girl could fill the stands, they saw I was good for the sport." She was voted to the Auto Racing All-American Team multiple times across the late 1970s and early 1980s.
A serious accident in 1984 crushed Muldowney's hands, pelvis, and legs, requiring approximately six operations and eighteen months of rehabilitation. She appeared on The Tonight Show with Johnny Carson in February 1986, still walking with a cane. She returned to competition in the late 1980s and continued racing through the 1990s, primarily in IHRA events and match races after losing major sponsorship. She ran select NHRA events toward the end of her career before retiring at the close of the 2003 season.
Longtime drag racer Fred Farndon described her as the best "natural" driver — in Top Fuel or Funny Car — he had ever seen.
Muldowney was inducted into the Motorsports Hall of Fame of America in 1990 and the International Motorsports Hall of Fame in 2004. The Automotive Hall of Fame inducted her in 2005. The NHRA ranked her fifth on its Top 50 Drivers list (1951–2000). In 2008, ESPN ranked her 21st on its list of the top 25 drivers of all time, citing her record as the first woman to win a major racing championship.
The 1983 biopic Heart Like a Wheel, starring Bonnie Bedelia, dramatised her life and career. Muldowney had mixed feelings about the film but acknowledged it was good for the sport.
She founded the charitable organization Shirley's Kids to help children in need in cities where drag racing is part of the community, and published her memoirs — Shirley Muldowney's Tales from the Track — in 2005.