Authorities initially said no one was injured, but after a morning news conference, San Diego police officer Anthony Carrasco said five people from a single family were admitted to hospital for smoke inhalation.
Another person was treated at a hospital for injuries sustained while climbing out of a window trying to flee. Two others were treated for minor injuries at the scene, Mr Carrasco said.
The number of fatalities has yet to be confirmed but according to PA Media, at least two are known to have been killed, although authorities could not definitively say if both of the dead were on the plane.