But a long-standing back injury has left her unable to join training partner Kamila Valieva and former Tutberidze charge Alexandra Trusova in the field despite painkilling injections.
The 20-year-old posted a message on her Instagram in Russian, saying, "Old back problems returned at the most inopportune moment. I hoped that the injections would help dull the pain, but in vain. You need to fight the cause, not the effect.
"I hope the fans understand the situation. I don't want to let anyone down. Thank you all for your support!
"I will have to miss the next stage of the Cup of Russia in Moscow. But we will do our best to prepare for other competitions. The season is still in full swing. Everything will be fine."
Medvedeva was seen at last month's Russian test skates before announcing her return to Tutberidze's Sambo-70 club in Moscow.
Russian Figure Skating Federation director Alexander Kogan told RIA Novosti: "She was examined by doctors and her old back injury has escalated so she will not take part in the competition and will go to the clinic for additional examination. The Federation wishes the athlete a speedy recovery."
This weekend's competition is the second of five 'stages' in the Cup of Russia with defending Russian champion Anna Shcherbakova, another Tutberidze protegee, winning the first in Syrzan three weeks ago.
Skaters accrue points across the five events - competing in a maximum two apiece - with the top 12 qualifying for the Russian Championships in Chelyabinsk from 23-27 December.
The remaining three competitions are in Sochi from 23-27 October, Kazan (8-12 November), and Moscow (5-8 December).
Reigning Grand Prix Final and European champion Alena Kostornaia, who followed Trusova in leaving Tutberidze for Evgeni Plushenko, is scheduled to make her first competitive outing of the season in Kazan.
Between the last two stages is Russia's stop on the 2020-21 ISU Grand Prix series, the Rostelecom Cup, in Moscow from 20-22 November.