He was 43.
"Sergei Ovchinnikov suddenly passed away at the team's (pre-season) training camp in Croatia," Dynamo said on their website (www.vldinamo.ru), without giving details of the cause of death.
Police in the town of Porec, where Dynamo had been training, said they were investigating the death of a foreign national who was staying as a guest in a hotel. Local media reported he was found hanging in a fourth-floor room.
Ovchinnikov was appointed national team coach last December and successfully guided Russia through qualification for the 2012 Olympics.
In London, the powerful Russian team, who won back-to-back world titles in 2006 and 2010, were considered leading medal contenders but lost in the quarter-finals to eventual winners Brazil after squandering six match points.
Former Russia coach Vladimir Kuzyutkin said his friend had committed suicide, and believed he may have been depressed.
"This is so stupid," Kuzyutkin told the Russian News Service. "He was my friend, my colleague. No one said a bad word about him. Yes, there was a failure at the Olympics, but to hell with that. I don’t know why he couldn’t cope with it.
"He took the Olympics very personally. I saw what he was going through and how upset he was after the defeat.
"He didn’t talk much. Even after victories he was always thinking about something and smoked a lot."