The 65,000-tonne ship, hailed as Britain's most advanced military vessel and which was only officially commissioned by the queen two weeks ago, has an issue with a shaft seal which was identified during sea trials, the MoD said.
"This is scheduled for repair while she is alongside at Portsmouth," a Royal Navy spokesman said. "It does not prevent her from sailing again and her sea trials programme will not be affected."
The Sun newspaper reported that the 280-metre (920-foot) warship was letting in 200 litres of water every hour and the fix would cost millions of pounds.
A defence source said the navy was aware the ship, which took eight years to build, had an issue when it was handed over by manufacturers and the Sun said the builders would have to foot the repair bill.
The Aircraft Carrier Alliance - a consortium including British engineering companies BAE Systems and Babcock, and the UK division of France's Thales - built the Queen Elizabeth and its sister aircraft carrier, the HMS Prince of Wales, as apart of a 6.2 billion pound project.
No one from the Aircraft Carrier Alliance was immediately available for comment.
"Every ship takes on water. That's why you have pumps," Chris Parry, former senior Royal Navy officer told Sky News.
On Tuesday, parliament's defence committee raised questions about the procurement of the F-35 fighter jets from a consortium led by Lockheed Martin which will eventually operate from the Queen Elizabeth.
The committee said there had been an "unacceptable lack of transparency" about the programme and the MoD had failed to provide details of the full cost of each aircraft which one newspaper had estimated could be as much as 155 million pounds.
"Our new aircraft carrier is the epitome of British design and dexterity, at the core of our efforts to build an Armed Forces fit for the future," British Defence Secretary Gavin Williamson said at the Queen Elizabeth's commissioning.
(Reporting by Michael Holden, Paul Sandle and James Davey; editing by Guy Faulconbridge)
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)