Although all 12 competing nations have already submitted their final rosters for the Sochi Games, the International Ice Hockey Federation gave Russia the go ahead to make another change.
Kokarev picked up the injury during his KHL side Dynamo Moscow's game with CSKA Moscow last week.
"We decided to call-up Aleksandr because he is an experienced hockey player, a world champion and can also play well in defense and at the face-offs," Russia's head coach Zinetula Bilyaletdinov said in a Russian Hockey Federation statement.
Svitov has found scoring difficult this season, with eight goals and 12 points in 46 games for AK Bars in the KHL, while he won the KHL's Gagarin Cup title with Salavat Yulaev in 2011.
The 31-year-old also had a stint in the NHL after he was drafted by the Tampa Bay Lightning in 2001.
Svitov is the second player to be called up by Russia following the initial squad selection. Aleksandr Semin of the Carolina Hurricanes was a late replacement for Sergei Soin of Dynamo Moscow, who had to pull out because of a leg injury.
(Reporting by Dmitriy Rogovitskiy; Editing by Justin Palmer)
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