The disturbance call came in around 6:45 pm on July 16 from near Commonwealth Avenue and Temple Street, according to the Los Angeles Police Department.
Officers located 49-year-old Herbert Vasquez in the rear bedroom of an apartment, where he refused to exit.
Police say officers opened fire on Vasquez when he advanced towards them with the machete.
Vasquez escaped out the bedroom window and ran down the street into a 7-Eleven convenience store. Officers used "less-than-lethal tools" to bring Vasquez into custody.
Vasquez was treated for injuries to his fingers. Police are not sure whether the injuries occurred during the officer-involved shooting.
Officers located a knife at the scene.
No officers or bystanders were injured.
The complete investigation will be reviewed by the Chief of Police, the Board of Police Commissioners and the Office of Inspector General.