Russian Olympic medallists are being made to quarantine for a week after returning from the Tokyo Games so that they can meet President Vladimir Putin, an athlete says.

Russians won 71 medals, including 20 golds, at the Olympics, a result feted as a victory at home despite the country competing without its flag and anthem because of doping sanctions.

Putin, 68, had two doses of COVID-19 vaccine, one in March and one in April, according to the Kremlin, but Moscow has continued to take pandemic precautions with regards to his health.

Before being vaccinated, Putin spent much of the pandemic running the country from his residence rather than the Kremlin, chairing video conference meetings instead of face-to-face encounters.

People who meet him in person have reported being required to quarantine.

"All Olympic champions and medallists have a meeting with the president when they return home," gymnast Angelina Melnikova, who won gold in the women's team event and bronze in the all-around and floor exercise, wrote in her Instagram stories.

"The meeting is planned for September 10, and because of COVID, which we are all fed up with, we have to be in quarantine for seven days."

Melnikova said athletes would undergo three COVID-19 tests in the hotel where they will be self-isolating.