Peter Weber (born 22 December 1938) is a German former gymnast. He competed in all artistic gymnastics events at the 1964 and 1968 Summer Olympics and won two bronze medals in the team classification. Individually his best achievement was 16th place in the rings in 1964. He also won a bronze medal with the East German team at the 1966 World Artistic Gymnastics Championships. Nationally, he won two titles in the rings, in 1964 and 1967, and one on the floor in 1965.