Dr. Hamid Mirshojae, 61, was ambushed and fatally shot by a single gunman after leaving his medical practice in the 5900 block of Topanga Canyon Boulevard on Aug. 23, according to the Los Angeles Police Department.
The shooter then fled on foot to an awaiting vehicle, police said.
Police and paramedics were called to the clinic and found Mirshojae in the parking lot suffering from a gunshot wound. He was pronounced dead at the scene.
On Tuesday, police arrested Evan Hardman, 41, of Tomball, Texas, and Ashley Rose Sweeting, 40, of Reseda.
Hardman was taken into custody in the greater Houston area and Sweeting was apprehended in the San Fernando Valley, police said. Both were arrested on suspicion of murder.
LAPD said its investigators worked closely with the FBI in L.A. and Houston. The U.S. Postal Inspection Service, the Harris County Sheriff's Office and the Houston Police Department assisted in the investigation.
Police did not release a motive for the shooting.
Anyone with information about the killing was urged to call the LAPD's Valley Homicide unit at (818) 374-9550.