Ostrowski did not enter professional baseball out of college, instead opting to teach for three years, leading to his being nicknamed "Professor" and "Specs" as a player. He was finally picked up at the age of 25 by the Boston Red Sox as an amateur free agent in 1941. The 6', 180 lb. left-hander began his professional career that season with the Centreville Red Sox. After missing the 1943-45 seasons while serving in the military during World War II, he played the 1946-47 seasons for the Louisville Colonels, the Red Sox' top farm team. In November 1947, he was part of an eight-player trade sending him to the Browns.
After starting the season in the minors with the Toledo Mud Hens, Ostrowski made his MLB debut on July 18, 1948 with the Browns. He was traded to the Yankees on June 15, 1950 as part of a seven-player trade, and pitched for them through 1952. After pitching for the Los Angeles Angels of the Pacific Coast League in 1953, he retired from professional baseball and returned to teaching.