Grabowski began his professional baseball career in 1922 with the St. Joseph Saints and in 1923 and 1924 with the Minneapolis Millers the American Association. He was traded to the Chicago White Sox in July 1924 and made his major league debut that month. He played for the White Sox for three years from 1924 to 1926, appearing in 89 games, 78 of them as a catcher. One of the games Grabowski caught was Ted Lyons' no-hitter on August 21, 1926.