Russian officials say two people have died after what they call an "emergency" on the bridge linking the occupied Crimean peninsula to Russia.
The incident has not been called an attack, but unconfirmed reports said explosions were heard early on Monday.
The Kerch bridge was opened in 2018 and enables road and rail travel between Russia and Crimea - Ukrainian territory held by Moscow's forces since 2014.
In October last year, it was partially closed following a major explosion.
The bridge - which is an important supply route - fully reopened in February.
Writing on Telegram, Sergey Aksyonov, the head of the Russian administration in Crimea, said: "Traffic was stopped on the Crimean bridge. An emergency occurred in the area of the 145th support from the [Russia side of the bridge].
"Measures are being taken to restore the situation. I ask residents and guests of the peninsula to refrain from traveling through the Crimean bridge and, for security reasons, choose an alternative land route through new regions."
This is how Russia refers to the Ukrainian territories it occupied last year and claims to have annexed.
Vyacheslav Gladkov, governor of the western Russian region of Belgorod, later said in his own Telegram statement that two people, the parents of a young girl, had died in the incident - which he, too, simply labelled an "emergency".
Russia's transport ministry has said the explosion did not damage the bridge's supports and that only the road surface had been affected.
BBC Russian reports that the ferry crossing that runs parallel to the bridge has been closed, while Russia state media agency TASS cites the local rail operator as saying train traffic may be affected.
Even now, the exact cause of the explosion last October remains unclear. Footage from the time showed a huge fireball erupting as a number of cars and lorries made their way across the bridge.
In the months before the incident, Ukrainian officials had repeatedly suggested that the bridge would be targeted, but in the days that followed, Kyiv declined to claim responsibility.
Oleksiy Danilov, head of Ukraine's National Security and Defence Council, posted a video of the bridge burning alongside a clip of Marilyn Monroe singing "Happy Birthday, Mr President". The explosion came the day after Russian president Vladimir Putin's 70th birthday.
The latest incident comes amid a much-anticipated counteroffensive by Ukrainian forces which aims to retake territory in southern and eastern Ukraine.
Monday is also the day on which a deal that has allowed grain to leave Ukrainian ports since it was brokered by the UN last year is set to expire.
Ukraine and Russia are among the world's top grain exporters, and the deal was reached amid fears that the war would lead to global food shortages, but Russia has so far refused to agree to an extension.
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