Russian officials say a lorry explosion then spread to oil tankers on the rail section.
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A large fire on the only crossing between the occupied Crimean peninsula and Russia was caused by a lorry explosion, Russian state media say.
The explosion on the road bridge then led to oil tankers on the rail section catching fire.
Footage showed a train ablaze, with the adjacent road crossing also appearing to have sustained damage.
Crimea was annexed in 2014 by Russia, which now uses the Kerch bridge to move military equipment into Ukraine.
Russian state media say traffic has been suspended.
“Today at 06:07 on the road part of the Crimean bridge from the side of the Taman Peninsula, a truck was blown up, which caused the ignition of seven fuel tanks of a railway train heading towards the Crimean peninsula,” Russian state agency RIA Novosti quotes the National Anti-Terrorism Committee (NAC) as saying.
An adviser to the head of Crimea, quoted by RIA Novosti, said work was under way to extinguish the fire.
The bridge across the Kerch Strait was opened by President Vladimir Putin in 2018, four years after Moscow illegally annexed Crimea.
It is said to be a key target for Ukrainian forces who have been attacking Russian logistics.
The crossing is more than 100 miles from Ukrainian-held territory. One explosives expert told the BBC said the fire was probably not caused by a missile.
“The lack of obvious blast / fragmentation damage on the road surface suggests that an air-delivered weapon was not used,” he said
He said it was possible that “a well-planned attack from below may have been the cause”.