The 21 MP-5 submachine guns and 12 large-caliber handguns were altered to fire blanks, but police were concerned that they could be converted back to take live ammunition.
The unguarded building was considered secure, LAPD Deputy Chief Michael Downing told the Los Angeles Times.
"I guess 'secure' is all relative now," he said. "It's embarrassing. ... It's a lesson learned."
The guns were moved Wednesday night to a multistory downtown building and stored in a locked box on the first floor, Downing said.
The building is about a mile from SWAT headquarters. It was donated to the department and has no alarm or surveillance systems.
SWAT members were scheduled to train at the building Thursday, but a police officer arriving at about 9 a.m. found that the weapons were missing, Downing said.
Thieves cut locks on an outside door and two inside doors and forced their way through a metal roll gate, he said.
The building was openly used as a SWAT training site and sometimes public demonstrations were held there. However, police have not ruled out the possibility that the theft might have involved police officers, Downing said.
"You wonder if this was a planned operation, what information they had, whether they were conducting surveillance," he said.
Since the theft, "appropriate measures" have been taken, Downing said, without providing details.
However, regional law enforcement agencies have been notified.
"This is a big deal," Downing said. "We're concerned. We want to recover them."