Russia's Northern Fleet officials said the blaze on the ship, the Admiral Kuznetsov, has been contained and the injured men have received medical attention.
The Admiral Kuznetsov was docked in Murmansk in northern Russia for an upgrade when the fire started amid welding work on Thursday morning.
Crew members and civilian specialists were aboard the ship at the time but have since been evacuated, dockyard representatives said.
The damage to the ship will be assessed later, the chief of the United Shipbuilding Corporation said.
The Admiral Kuznetsov was used in the Mediterranean Sea to launch carrier-borne Russian combat missions on targets in Syria.
The fire is the second major emergency on the ship since it docked for repairs in April 2018. In October 2018, a crane collapsed on the carrier's deck, injuring four people.