Police said the pair's car stopped some 100 metres before a roadside checkpoint at around 1.30am near the city of Baar, then proceeded to drive up to officers — who found the 27-year-old woman naked at the wheel.
According to officers, the couple soon admitted to having switched seats for fear that the 29-year-old man would be detained for the second time in two days for driving without a license.
Police said the woman refused to explain the reason for her nudity by invoking her right to remain silent.
The man, who saw his car seized in the incident, is now awaiting a court hearing where he will be expected to explain his actions.
Zug police said the man was stopped for allegedly driving while drunk on Saturday night.
He was locked up briefly after becoming abusive to officers who discovered he was driving without a valid license.
The man was later released before being apprehended again on Monday.
He now faces various violations of the road traffic act, Zug police said.
The woman was not charged.