The woman was shot in the arm and will recover. Her name was not released.
Investigators were interviewing the 48-year-old suspect Friday morning and did not release his name.
The shooting happened about 1:30 a.m. inside the man's room at the Starlite Motel, 10000 MacArthur Boulevard. Police said he had been staying at the motel since last month.
The woman had also been staying at the motel in another room for about a week, police said.
The woman went to the man's room where an argument ensued and she was shot, Sgt. Todd Mork said. She ran from the room seeking help and police, who also were alerted by Shotspotter technology, responded.
The man was arrested, and a gun recovered. Police were trying to establish what the argument was about and how well the two knew each other.