No foul play was suspected but authorities haven't given a cause for the blaze at the Mickey & Friends Parking Structure.
Four cars were destroyed and four more had major damage from the fire, which brought losses estimated at $180,000, the Anaheim Police Department said. Thousands of cars are tightly packed into the structure daily.
Seven Disney employees were treated for smoke inhalation, but only one was taken to a hospital and none of the injuries was life-threatening, Anaheim fire Sgt Daron Wyatt said.
"A lot of people are just tired; they've been here all day. It's more of a nuisance than anything," Darren Clark, whose family of four couldn't get to their car because of the shutdown, told KNBC-TV. "I'm kind of hoping it's not my vehicle."
The Mickey & Friends Structure, with sections named for Disney characters and trams that take visitors to the entrance to the Disney Resort's two theme parks, is a familiar spot for millions of visitors who pay $18 to park.