The crash occurred in the 300 block of North La Brea Avenue around 7:20 a.m.
Investigators say the car was trying to pass another vehicle when it lost control.
Two people were transported to a local hospital. Los Angeles Fire Department spokeswoman Katherine Main said an adult male was listed in grave condition, and an adult female was listed in fair condition.
The extent of the damage to the building remains unknown.
Inspectors with the Department of Building Safety were immediately notified.