A receiver at Baylor University, Gremminger was converted to cornerback. He played for the Packers from 1956-65 and finished with 28 interceptions (eighth on the team's all-time list) and seven fumble recoveries. He played one season with the Los Angeles Rams before retiring.
The 6-foot-1, 195-pound Gremminger played in the 1960, '61, '62 and '65 NFL Championship games. He intercepted a pass from quarterback Y.A. Tittle in the '61 title game as the Packers beat the Giants 37-0.
Gremminger is survived by two daughters and five grandchildren.