In 1972, at the age of 19, Meyer made his professional baseball debut in the Detroit Tigers minor league organization. He was assigned to play with the Bristol Tigers of the rookie-level Appalachian League, where he batted .396 with 93 hits, 11 doubles, six triples, and 14 home runs in 65 games played. On defense, he played second and third base. He led the league in batting average, hits, and total bases (158) that season. During his second professional season in 1973, Meyer was assigned to the Lakeland Tigers of the Class-A Florida State League. With Lakeland, he batted .241 with 114 hits, 17 doubles, six triples, and 10 home runs in 133 games played. In the field, Meyer only played second base. It would later prove to be his last professional season playing at that position.