The blaze was reported around 5 p.m. at Fourth and China Basin streets. The apartment complex was still under construction.
About 150 firefighters responded to the scene, and teams were expected to remain there throughout the night. One firefighter was taken to the hospital to be treated for a minor burn, according to KGO-TV.
KGO says the MB360 apartments were set to open in August. According to fire officials, fire-suppression systems had not yet been installed in the building, making it harder for firefighters.
The cause of the fire remains under investigation.
KGO-TV and The Associated Press contributed to this report.