PC Adam Zaman, 28, allegedly committed the offence on 24 October while off-duty in the City of London.
The officer, who is based in the force’s East Area Command Unit, has been remanded in custody ahead of an appearance at Westminster Magistrates’ Court on Wednesday afternoon.
A spokesperson for the Metropolitan Police said PC Zaman had been suspended from duty.
Its Directorate of Professional Standards has been informed and the matter has been referred to the Independent Office for Police Conduct.
Detective Chief Superintendent Paul Trevers, Policing Commander for the East Area Command Unit, said: “I recognise that the public will be concerned to hear that a serving police officer has been charged with such a serious offence. We absolutely share that concern.
“We acted swiftly when this allegation was reported to us and have fully supported what continues to be a thorough investigation by detectives from the City of London Police. Specialist support is being provided to the complainant.
“PC Zaman has now been charged and it is important that criminal proceedings are allowed to take their course. Nothing should be said or reported which could put the integrity of those proceedings at risk.”