Some wounded people have been seen lying on stretchers outside the college, which provides vocational training to teenage pupils.
In a video posted on the Internet, a woman identified as the director of the college, Olga Grebennikova, said there were "many corpses, many corpses of children" and called it "a real terrorist act".
The blast at a college in the Crimean peninsula's city of Kerch was an act of terrorism carried out using a home-made bomb, the first deputy head of the National Guard Sergei Melikov said on Wednesday, according to TASS news agency.
Russian Federation annexed Crimea from Ukraine in 2014, a move that triggered Western sanctions and worldwide condemnation.
Dmitry Peskov, spokesman for Russian President Vladimir Putin, told reporters that officials are looking into the possibililty it was a terrorist attack. Preliminary figures are 50 injured and 10 dead.
"At the moment, there are 13 dead and about 50 wounded, a lot of them teenagers".
Emergency services and ambulance cars are working at the scene of the accident. Located in the easternmost tip of Crimea's Kerch peninsula, the area is connected to mainland Russian Federation by the newly-built massive Crimean bridge.
Rights activists say Russian authorities have used the courts and law enforcement to conduct a campaign of reprisals against Crimeans who opposed the takeover. Earlier, emergency officials said the explosion was believed to have been caused by a gas canister explosion.
The wars were followed by an Islamist insurgency in the North Caucasus region, east of Crimea, and insurgents have claimed responsibility or been blamed for most of the bombings and other attacks in Russian Federation over the years.