The crash was reported at 10:53 a.m., according to police.
Public Works Department spokeswoman Gloria Chan said the truck was able to clear the entrance to the tunnel, but because the tunnel's ceiling becomes lower inside, it then hit the ceiling.
Chan said the truck scraped off light fixtures and tiles from the tunnel ceiling.
She said eastbound lanes of the tunnel reopened at about 9:45 p.m. after crews determined there was no structural damage. Crews are expected to return to the tunnel at a later date to confirm there is no structural damage and work on other repairs.
According to Chan, 13-foot-6-inch clearance signs are clearly posted at each end of the tunnel.
The tunnel remained open in the westbound direction throughout the day.