The professional dancer, who partnered Phil Tufnell, Gavin Henson, Dan Lobb and Simon Webbe during her time on the show, has been axed to make way for a new face, according to The Sun.
A BBC spokeswoman said: "We'd like to thank Katya for her wonderful contribution to the show. She will very much remain part of the Strictly family."
A source told the paper that the show's new executive producers Glenn Coomber and Andrea Hamilton have decided to retain all the other professional dancers.
"Glen and Andrea wanted to meet the dancers and hear why they wanted to do this year's show," the insider said.
"They always knew they wanted to bring in fresh talent but it was about deciding who would have to make way and they decided to give Katya the boot.
"She is not as high profile as some of the other female dancers, although it was a close call and it was nothing personal against her.
"Producers are excited about the new dancer, who they hope will shake up the show and keep the other professionals on their toes."
James Jordan, who was involved in a row over marking with judge Craig Revel Horwood on the 2011 series, will apparently return to the show.
"All the other dancers are back, including James, who many thought might be axed because of his row with Craig," the source added.
"But producers want as much drama as possible this year and bringing James back to face Craig could provide that."
Strictly Come Dancing will return to BBC One later this year with new judge Darcey Bussell replacing Alesha Dixon.
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Watch Katya Virshilas dance the Viennese Waltz with Gavin Henson on Strictly Come Dancing below: