CSKA GM Sergei Fedorov, who played 18 seasons in the NHL and won three Stanley Cup championships, announced the move on Monday.
Former Pittsburgh Penguins forward Alexei Morozov will replace Radulov as captain.
Morozov, 36, signed with CSKA in May after nine seasons with Ak Bars Kazan.
"Morozov's a man with great experience," Fedorov said. "I think this is a logical move. He's the most successful, most respected player on our team."
Fedorov wouldn't get into details as to why Radulov was removed as captain, but indicated it related to off-ice issues.
"The last captain had problems with discipline," said Fedorov. "Will it hurt the previous captain? He shouldn't and cannot be hurt."
Radulov, 27, returned to the Predators during the 2011-12 season after three and a half seasons with the KHL's Ufa Salavat Yulayev. He got into some trouble after he and then-teammate Andrei Kostitsyn broke curfew after spending too much time at a bar in Scottsdale, Arizona during the team's playoff series against the Phoenix Coyotes.