Mr Khan said in an interview with Hard Talk Pakistan, a local news outlet, he had discussed possible punishments for the alleged perpetrator with ministers in his cabinet.
“I think he (the rapist) should be hanged publicly,” the Prime Minister told the program on Monday.
“Rapists and child molesters should have public hanging.”
“You do not know the real statistics as well, because it’s under-reported,” he said.
“People do not report it due to being scared or ashamed, women are ashamed, no one wants to tell.”
The woman had called a helpline and was waiting for the police to arrive with fuel when two men raped and robbed her, officials said.
Police have arrested three men, including one of the alleged rapists.
The other, described by police as the mastermind of the group, remains at large.
The case is being investigated by Lahore Police.