Dmitry Peskov, spokesman for Russian President Vladimir Putin, told reporters that officials are investigating.
State news agencies quoted the Russian National Counterterrorism Committee (NAK) as saying it was caused by an unidentified explosive device.
The Tass news agency reported that most of the victims were students and quoting a National Guard official who said the incident was a terror attack.
The director of the vocational college, in the Black Sea city of Kerch, told local media that after the blast a gunman went through the school killing anyone he could find, and that children's bodies were "everywhere".
Photographs from the scene of the blast posted by local media outlet Kerch.FM showed that the ground floor windows of the two-story building had been blown out, and that debris from the building was lying on the floor outside. "Eight ambulance crews are working at the site and air medical services are involved", the Crimean Ministry of Health said in a statement. Preliminary figures are 50 injured and 10 dead.
Pupils and college staff were among those killed, she said.
"At the moment, there are 13 dead and about 50 wounded, a lot of them teenagers".
Crimean authorities said initial information suggests the blast was caused by a "gas canister" that "blew up" inside the college's canteen.
Kerch is the site of the western end of a newly built bridge linking Russian Federation to Crimea, which it took over by force after Moscow-friendly Ukrainian President Viktor Yanukovych was pushed from power by pro-European protests in Kyiv.