The break-in occurred about 4:30 a.m. at the dispensary near the intersection of Pico Boulevard and Spaulding Avenue, said LAPD Officer Jack Richter.
Officers responding to an alarm saw one of the suspects running away from the area and arrested the individual.
Richter said the owner of the dispensary called police to say he was heading to the location and said video streaming through his smartphone showed one person was still inside the business.
Richter said that person became locked in and couldn't get out.
"I call it self-barricade," Richter said, adding that the second suspect was also arrested.
Richter said a third person in a vehicle was believed to be involved but fled the area before officers arrived.
The names of the two suspects in custody were not immediately available.