Conservative leader Kemi Badenoch has called for a “full investigation”.
In a social media post, Badenoch said if the chancellor broke the law, the prime minister must “show he has the backbone to act”.
The family home in London was put up for rent after Labour won the election in July 2024 for £3,200 a month.
It is in an area where Southwark Council requires private landlords to hold a “selective licence”.
Selective licences are required by some local councils, and are not a nationwide scheme in England.
The licences require landlords to meet set standards – normally aimed at raising housing quality, fighting crime and boosting housing demand.
The council’s website states: “You can be prosecuted or fined if you’re a landlord or managing agent for a property that needs a licence and do not get one.”
A spokesperson for Rachel Reeves said: “Since becoming chancellor Rachel Reeves has rented out her family home through a lettings agency.
“She had not been made aware of the licencing requirement, but as soon as it was brought to her attention she took immediate action and has applied for the licence.
“This was an inadvertent mistake and in the spirit of transparency she has made the prime minister, the Independent Adviser on Ministerial Standards and the Parliamentary Commissioner for Standards aware.”
Writing on social media, Badenoch said Sir Keir “once said ‘lawmakers can’t be lawbreakers’. If, as it appears, the chancellor has broken the law, then he will have to show he has the backbone to act.”
The Liberal Democrats’ deputy leader Daisy Cooper said: “The chancellor is meant to be delivering growth but the only thing she appears to be growing is the government’s list of scandals.
“Just weeks before the Budget, this risks seriously undermining confidence in this government and its ability to focus on the urgent tasks at hand.”