Captain Frederick van Wyk of the Western Cape police said that the constable arrived at the airport around 6.30pm and went to the food-court to speak to his partner at one of the restaurants.
“It is alleged that an argument ensued and he shot his partner and two other employees at the food outlet,” he said.
“The man then turned the gun on himself, fatally wounding him.”
An inquest docket and attempted murder dockets were opened.
Van Wyk said that investigations continued.
Airports Company SA at Cape Town International Airport earlier confirmed the shooting.
“This is a tragic event and our condolences go out to the friends and family. We can now confirm that three other people were injured,” spokeswoman Deidre Davids said in statement.
The area was cordoned off and was declared a crime scene.
Davids said that airport operations had not been affected because the shooting happened in a small section of the airport.