In the routine, former Olympic ice skater Tatiana Navka, who is also the the wife of a spokesman to Russian President Vladimir Putin, and actor Andrei Burkovsky wore striped costumes with yellow Star of David patches resembling the uniforms of inmates imprisoned in Nazi concentration camps.
Navka and Burkovsky performed a routine to a fragment of the soundtrack of Roberto Benigni's film "Life is Beautiful' that recounts the story of a Jewish-Italian family sent to a concentration camp during World War II".
Six million Jewish people are estimated to have been killed during the Holocaust.
The programme, "Ice Age", is broadcast on Russian State-run station Channel One.
Navka posted a series of pictures of the routine on her Instagram account, where critics lashed out at the figure skater and demanded an apology. Our children need to know and remember that bad time, which I hope, God willing, they will never know.
"Have you gone mad?"
The pair's skating routine was awarded maximum points by the TV show's judges. The audience erupting in applause...
The routine was choreographed by 2002 Olympic silver medalist Ilya Averbukh, who is Jewish. "No taste, no, tact, no understanding", wrote viewer Mihael Ratinsky on the Channel One website.
There were several Instagram users who were amazed at her performance, such as one user who said, "Beautiful piece of work. This is blasphemy", wrote another viewer, Viki Reznik, in a comment to a YouTube video of the routine that had been viewed more than 37,000 times on Monday, to mostly negative reactions.
Head of the Moscow-based Holocaust Fund Alla Gerber said in an interview with Govorit Moskva radio station that it was "very complex" to depict the Holocaust appropriately.
Navka, 41, won gold in ice-dancing at the 2006 Olympics and has since become a prominent television personality.