More than 200 crew members were assessed for smoke inhalation and later returned to duty after the fire broke out on 2 March, US officials said.
One sailor was medically evacuated and is in a stable condition, while two others were treated for minor injuries.
The fire prompted a major damage control response, with sailors working for hours to contain the blaze and ensure it had not spread to other parts of the ship, officials said.
Smoke damage spread to sleeping quarters, leaving more than 100 beds unusable, according to authorities. Replacement cots have been arranged, and additional mattresses and clothing were sent to the ship after its laundry facilities were wiped out.
A spokesperson for the US Fifth Fleet said the ship remained operational. The cause of the fire is being investigated.
The Ford will sail to Naval Support Activity Souda Bay in Crete for more than a week of repairs, a US official told USNI News, a site specialising in the US Navy.
In January, the vessel suffered a malfunction in its toilet system, with US media reporting clogged toilets and long lines for restrooms on the ship.
The Navy acknowledged there had been some issues, citing the vessel’s leadership as saying “clog incidents are addressed promptly by trained damage control and engineering personnel, with minimal downtime”.