Journalist Lyudmila Telen, an activist campaigning for Bakhmina's release from prison, said on Ekho Moskvy radio that both mother and baby were doing well.
"She is feeling satisfactory, the baby is also in good health," Telen said.
Bakhmina, 39, former deputy head of the legal department of the now defunct oil company's Moscow unit, has served almost four years out of a six and a half year sentence. Bakhmina, who already had two children, was transferred from a prison in central Russia to a maternity clinic near Moscow earlier this month.
The Supreme Court is due to consider Bakhmina's parole appeal which was rejected in September by a court in Mordova, despite her pregnancy and testimony of her good behavior while in prison. It was the second time the court had rejected Bakhmina's parole request.
Legal proceedings launched against Yukos in 2003, seen by many as politically motivated, resulted in the conviction of Bakhmina and other executives and shareholders of what was Russia's largest oil producer, including founder and CEO Mikhail Khodorkovsky.
