The crash happened around 4:45 a.m. at the Harbor Division station.
Officials said the driver maneuvered her sedan past barriers and smashed into the front glass doors of the lobby, coming to a stop fully inside the station.
The lobby was closed at the time and no one was inside.
Surveillance video released by the department shows the vehicle driving fully into the lobby around 4:36 a.m. An officer comes out to speak with her and after a few minutes, she hits reverse with her door open, dragging the officer back a few feet before he can jump out of the way.
She was unable to escape because of the barriers outside the station. Officers took her into custody.
Both she and the baby were sent to a hospital for evaluation but they were not believed to be seriously injured.
Police say it appears the woman was driving under the influence. It's not clear yet if she intentionally crashed into the station.
Officers have not determined what if any charges she may face. Her name has not been disclosed.