The satellite was placed into orbit early Thursday, the ITAR-TASS news agency quoted the spokesman as saying.
Russia has already launched two military satellites this year, and plans to launch nine more by the end of the year, the defense ministry said last month.
The satellites, which will have a lifespan of seven to 10 years, will be launched from the Baikonur cosmodrome in the former Soviet republic of Kazakhstan in central Asia, and from the Plesetsk space base.
The Russian military intends over the next few years to move activities from Baikonur to Plesetsk.
Currently almost three quarters of Russia's military satellites are launched from Baikonur, which is leased by Kazakhstan to Russia for 115 million dollars (100 million euros) a year.