The plane, which was on its way to Latakia in Syria, was carrying 81 passengers and 10 crew members, Interfax news agency reported.
The Tu-154 is a Soviet-designed three-engine airliner.
In April 2010, many high-ranking Polish officials, including then president Lech Kaczynski, were killed when a Tu-154 airliner went down in thick fog while approaching the Smolensk airport in western Russia.
Al Jazeera's Natasha Ghoneim, reporting from Moscow, said the plane disappeared from radar only minutes after takeoff.
"Reports here in Moscow are saying that the passengers included journalists and military personnel, in addition to members of the famous Alexandrov Ensemble," Ghoneim said.
The Russian defence ministry said that the Alexandrov Ensemble was to perform at the Khmeimim airbase, Russia's main base of operations for its military campaign in support of the Syrian government.
Russia has been supporting its longtime ally Syria with a bombing campaign against rebel groups for more than a year.
Rescue services of aviation units of the Southern Military District in Krasnodar and neighbouring regions were engaged in the search for the plane wreckage, the defence ministry said.