Images from the bridge showed a fiercely burning fire engulfing at least two railway carriages from a train on the bridge, accompanied by a vast column of black smoke.
The explosion, which witnesses said could be heard kilometres away, took place around 6 a.m. on Saturday while a train was crossing the bridge.
A truck was blown up on the Crimean Bridge, the National Anti-Terrorist Committee said.
"Today, at 6:07 a.m., a truck was blown up on the motorway section of the Crimean Bridge from the Taman Peninsula, which caused seven fuel tanks of a train travelling to the Crimean peninsula to go up in flames. Two motorway sections of the bridge have partially collapsed. The arch over the land part of the bridge has not been damaged," the report says.
The cause of the explosion is now being investigated, according to Sputnik.
The Crimean Bridge has not been seriously damaged so repairs will be made promptly, the head of the Crimean parliament, Vladimir Konstantinov, said.
"Ukrainian vandals managed to reach the Crimean Bridge with their bloody hands. They now have something to be proud of: for 23 years of their management, they failed to build anything worthy of attention in Crimea, but they managed to damage the canvas of the Russian bridge. This is the whole essence of the Kyiv regime and the Ukrainian state. Death and destruction are the only things of which they are capable," Konstantinov wrote on his Telegram channel.
The movement of ships in the Kerch Strait did not stop despite a fire on the Crimean Bridge, the Russian Federal Agency for Sea and Inland Water Transport (Rosmorrechflot) said.
Russian President Vladimir Putin has ordered the formation of a government commission to examine the Crimean Bridge incident, Kremlin spokesman Dmitry Peskov said.
There are no forecasts on how long it will take to repair the Crimean bridge, Kremlin spokesman Dmitry Peskov said.
According to the head of the Republic of Crimea Sergey Aksenov, one motorway section of the bridge is "visually intact".
A Ukrainian presidential advisor posted a message on Twitter after conflicting reports of an explosion or fire on Saturday that damaged the bridge connecting the Russian mainland to the peninsula of Crimea, calling it "the beginning" but not directly claiming Ukrainian responsibility.
ZZ/PR