“He will be returning to the country once his doctors have completed their treatment,” its statement said.
The announcement comes a day after the Constitutional Court upheld a ruling that Zuma was granted medical parole unlawfully in September 2021.
He had been released from prison after serving less than eight weeks of a 15-month sentence.
Zuma, now aged 81, had been jailed for failing to attend an inquiry into corruption during his presidency.
He was forced to resign because of the allegations in 2018 after nine years in office – but has repeatedly maintained he is the victim of a political conspiracy.
Mzwanele Manyi, spokesperson for the Jacob G Foundation, said it was issuing the information about Zuma’s trip to Russia because of media speculation.
“Although the trip was private, it was not a secret as incorrectly suggested,” he said, adding that Zuma and his team had travelled “on a commercial flight full of passengers”.
The statement ended without saying when the former president would be returning to South Africa: “The foundation wishes its patron good health and a safe return home whenever the doctors release him.”