Khan said in an interview with Hard Talk Pakistan on 92 News that he had discussed possible punishments for the alleged perpetrator with ministers in his cabinet.
"I think he (the rapist) should be hanged publicly. Rapists and child molesters should have public hanging. You do not know the real statistics as well, because it's under-reported. People do not report it due to being scared or ashamed, women are ashamed, no one wants to tell," Khan told interviewer Moeed Pirzada on Monday.
However, Khan said that public hanging would not be internationally acceptable and could affect Pakistan's trading relationship with the European Union. He suggested instead that rapists and child molesters "undergo chemical castration, or surgery be performed so they cannot do anything in future."
Last Thursday, a woman lodged a complaint in Lahore, alleging that she had been gang-raped that night by two men after she ran out of fuel and her car broke down, according to the First Information Report (FIR).
The woman had called a helpline and was waiting for the police to arrive with fuel when two men raped and robbed her, according to officials.
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.