The warship had been successfully extracted from the dock before it completely sank.
Moscow: Russia's only aircraft carrier was damaged while undergoing repairs in the north of the country after the floating dock holding it sank in the early hours of Tuesday morning and a crane crashed onto its deck.
The Admiral Kuznetsov has seen action in Russia's military campaign in Syria in support of President Bashar al-Assad with its planes carrying out air strikes against rebel forces.
It was being overhauled on one of the world's biggest floating docks in the icy waters of the Kola Bay near Murmansk close to where Russia's Northern Fleet is based and was due to go back into service in 2021.
Maria Kovtun, Murmansk's governor, said in a statement that a rescue operation had been launched and 71 people evacuated after the floating dock holding the ship had begun to sink.
The warship had been successfully extracted from the dock before it completely sank, she said.
Investigators, who said they had opened a criminal investigation into the incident that would look at whether safety rules had been violated, said one person was missing and four others were being treated for hypothermia after being plucked out of the water.
Alexei Rakhmanov, head of Russia's United Shipbuilding Corporation, told the TASS news agency that the ship's hull and deck had been damaged, although what he called the vessel's vitally important parts had not been harmed.
Yevgeny Gladyshev, a spokesman for the shipbuilding factory which operated the floating dock, told the RIA news agency that unspecified equipment had been damaged but that much of the deck had been spared because it had been removed during repairs.
The floating dock had been hit by a power outage which had caused its water tanks to fill up rapidly, prompting it to sink, the factory said.
The Admiral Kuznetsov gained notoriety in Britain when then Secretary of Defence Michael Fallon dubbed it the "ship of shame" in 2017 when it passed through waters close to the English coast on its way back from the Mediterranean belching black smoke.