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.
Notable deaths of 2014 [PHOTOS]
UPI Sports Results for September 19, 2014