Kudukhov, 27, was killed when his vehicle collided with a truck on a highway near the southern Russian city of Armavir.
The wrestling federation's written statement did not provide any further details on the accident.
Kudukhov won a bronze medal in freestyle wrestling at the 2008 Olympics in Beijing and a silver medal at the London games last year. He also won world championships in the event in 2007, 2009, 2010 and 2011, Russia's RIA Novosti news agency said.
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