South Africa's Police Minister Bheki Cele says there can't be a "grain of explanation" to defend Wednesday's killing of a bystander as police dispersed protesting university students.

The minister said "someone went crazy" during the protest in Johannesburg leading to the shooting.

The victim, identified as Mthokozisi Ntumba, was shot while coming out of a clinic and died at the scene, according to media reports.

Mr Cele visited the victim's family on Thursday and said the police watchdog had started an investigation.

"He's a young man, even I saw his photo. He was working for the department of human settlement and had just gained his master's degree. He's a father of three, he's got a very young wife," he told journalists.

"It's a sad situation to look at, it's something that you can't really even be able to live with as a human being."

The minister also said accusations of police excesses when dealing with black populations were "becoming difficult to defend".