It happened west of downtown around 2:15 a.m. and ended on Washington Ave. near I-10.
The man was spotted by off-duty officers who were working a second job when he yelled derogatory statements at them, according to Houston police.
The chase lasted around four minutes before the driver collided with the building that had customers and employees inside at the time.
No one was hurt and the driver was arrested and was believed to have been intoxicated, police said.
The 24-hour restaurant had to be closed due to the damage from the crash.