Officials said an "unidentified explosive device" detonated at the technical college in Kerch, where Russian Federation has built a bridge between the peninsula and Russian Federation.
Initial reports on the blast said it was caused by a gas explosion.
"The majority of them are teenagers", the committee said in a statement, adding that the metallic device was planted in the school's cafeteria.
Olga Grebennikova, the college's director, told Crimean media outlets outside the college that someone had blown themselves up inside the college.
The Kremlin's spokesman, Dmitry Peskov, told reporters that President Vladimir Putin has expressed his condolences to the victims and ordered emergency services to provide assistance. He said he looked out and saw a young man with a rifle shooting at people.
Sergei Aksyonov, Moscow's senior official in Crimea, said 18 people were killed and dozens more were injured.
The woman, speaking on a mobile phone, says that shortly after she left the college for a meeting elsewhere, assailants attacked the school, throwing explosive devices and firing guns.
The Komsomolskaya Pravda newspaper quoted student Semyon Gavrilov, who said he fell asleep during a lecture and woke up to the sound of shooting.
"I locked the door, hoping he wouldn't hear me", the paper quoted Gavrilov as saying.
Dramatic photos published by local media show the windows on the ground floor of the two-storey building have been shattered, with debris scattered across the floor.
Russian Federation annexed Crimea from Ukraine in 2014, prompting global condemnation and Western sanctions.
State-run Russian news agency RIA Novosti, citing regional emergency medical officials, said that according to preliminary information, 10 people were killed.