‘The main black box was found at 5:42 am Moscow time (0242 GMT) 1,600 metres from the shore at a depth of 17 metres,’ the agencies quoted the ministry as saying.
The agencies reported that the black box would be flown to the Moscow region to be deciphered by experts.
The ministry also said that 12 bodies and 156 body fragments had been recovered from the water since the crash.
Authorities have said that the human bodies and remains found would be sent to Moscow for identification.
The Tu-154 jet, whose passengers included more than 60 members of the internationally-renowned Red Army Choir, was heading to Russia's military base in Syria when it went down off the coast of the resort city of Sochi minutes after take-off on Sunday.
Authorities have dismissed terrorism as a possible cause for the crash.
Russia's federal security service said Monday it was focusing on pilot error, a technical fault, bad fuel and a foreign object in the engine as the four main scenarios that could explain the crash.