The blast on the bridge over the Kerch Strait, for which Russia did not immediately assign blame, prompted gleeful messages from Ukrainian officials but no direct claim of responsibility.
Russian officials said three people had been killed, probably the occupants of a car travelling near a truck that blew up.
Despite the damage, limited road traffic resumed about 10 hours after the blast on Saturday and the Transport Ministry said on Saturday rail traffic could continue.
Russia seized Crimea from Ukraine in 2014 and the 19km Crimean Bridge linking it to Russia's transport network was opened with great fanfare four years later by President Vladimir Putin.
It now represents a major artery for the Russian forces who have taken control of most of southern Ukraine's Kherson region, and for the naval port of Sevastopol, whose governor told locals: "Keep calm. Don't panic."
It was not yet clear if the blast was a deliberate attack but the damage to such high-profile infrastructure came at a time when Russia has suffered several battlefield defeats and could further cloud the Kremlin's messages of reassurance to its public that the conflict is going to plan.
It also took place a day after Putin's 70th birthday, and coincided with the naming of Air Force General Sergei Surovikin, Russia's third senior military appointment in the space of a week, to take overall charge of the invasion effort.
The change follows the reported sacking earlier this week of the commanders of two of Russia's five military regions, as its forces have suffered a series of dramatic reverses in northeastern and southern Ukraine in recent weeks.
The ministry did not say who, if anyone, Surovikin was replacing.
Surovikin, 55, has led Russia's Air and Space Forces since 2017.
According to the ministry's website, he commanded a guards division stationed in Chechnya in 2004, during Russia's war against Islamist rebels, and was awarded a medal for his service in Syria in 2017.
The head of Ukraine's National Security and Defence Council, Oleksiy Danilov, posted a video of the burning bridge on social media on Saturday alongside a video of Marilyn Monroe singing "Happy birthday, Mr President".
Since the start of the invasion on February 24, Ukrainian officials have made regular allusions to their desire to destroy the bridge, seen in Ukraine as a symbol of Russia's occupation of Crimea.
Ukraine's postal service said on Saturday it would print a special stamp to commemorate the blast.
Russia's Defence Ministry said in a statement that its forces in southern Ukraine could be "fully supplied" through existing land and sea routes.
The Transport Ministry said road traffic for light vehicles and buses had resumed in alternating directions on the intact half of the roadway.
Goods vehicles were being referred to a ferry service.
Foreign Ministry spokeswoman Maria Zakharova said Ukraine's reaction to the destruction of civilian infrastructure "testifies to its terrorist nature".
The Russian National Anti-Terrorism Committee said a freight truck had blown up on the bridge's roadway at 6.07am, causing seven fuel tanker wagons to catch fire on a train heading for the peninsula on the bridge's upper level.
It said two spans of road bridge had partially collapsed but that the arch spanning the channel through which ships travel between the Black Sea and Azov Sea was not damaged.
Images posted by the Russian Investigative Committee showed one half of the roadway blown away and the other half still attached.
Others taken from a distance showed thick smoke pouring from part of the bridge.
An adviser to Ukrainian President Volodymyr Zelenskiy posted a message on Twitter saying the incident was just "the beginning" but stopped short of saying Ukrainian forces were responsible for the blast.
"Everything illegal must be destroyed, everything that is stolen must be returned to Ukraine, everything occupied by Russia must be expelled," Mykhailo Podolyak wrote.
