Bykovsky started flying lessons at the age of 16, joined the army in 1952, and in 1959 became a jet fighter pilot. In the early 1960s he was trained as a cosmonaut at the Zhukovsky Military Engineering Academy.

On June 16, 1963, after Bykovsky had been in orbit two days, the Soviet Union launched Vostok 6, carrying Valentina Tereshkova (Tereshkova, Valentina), the first woman to travel in space. The two ships held parallel orbits, at one point approaching to within 3 miles (5 km) of one another, but did not rendezvous. They returned to Earth three hours apart.

Bykovsky was made a member of the Communist Party on June 18, while still in orbit, and after his return he received his country's highest honour, Hero of the Soviet Union. He was one of the few men to receive the Soviet Union's highest combat award during peacetime, the Order of the Red Star, presumably for air-combat action in a border incident.

He was chief of cosmonaut training for the Apollo- Soyuz Test Project, which was carried out in July 1975, and was command pilot of Soyuz 22, a 190-hour flight that began on Sept. 15, 1976.