The 280 metres-long and with an estimated 50-year working life, the carrier is the biggest and most powerful built by the UK.
The Royal Navy's future flagship, which was commissioned by Queen Elizabeth II on December 7 in Portsmouth, has a problem with one of its propeller shafts.
The fault on the carrier was first identified during sea trials, the BBC reported.
According to the Sun newspaper, HMS Queen Elizabeth has been taking on up to 200 litres of sea water every hour - the capacity of fish tank measuring 100cm x 50cm x 40cm - because of the fault.
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The Navy spokesman said: "An issue with a shaft seal has been identified during HMS Queen Elizabeth's sea trials; this is scheduled for repair while she is alongside at Portsmouth.
"It does not prevent her from sailing again and her sea trials programme will not be affected," he said.
British Defence Secretary Gavin Williamson said the cost of the repair would be funded by the contractors that built it.
"This is the reason why we have the sea trials, to make sure that everything is working absolutely perfectly. This is something that work is currently ongoing to deal with," he said.
HMS Queen Elizabeth was built by the Aircraft Carrier Alliance, a grouping of BAE Systems, Babcock and Thales.
Blocks were completed at six yards - before being assembled at Rosyth Dockyard in Fife.
The company said: "It is normal practice for a volume of work and defect resolution to continue following vessel acceptance. This will be completed prior to the nation's flagship recommencing her programme at sea in 2018."
Rear Admiral Chris Parry, a former director of operational capability at the Ministry of Defence, said the headlines were "very embarrassing" but the leak "in reality is no big deal".
"You expect to take some water in when you're operating a warship at sea," he told the BBC, adding that was why they are equipped with pumps.
The HMS Queen Elizabeth entered its home port of Portsmouth for the first time in August after starting two months of sea trials from Rosyth.
A second carrier, HMS Prince of Wales, is externally complete but it will take 18 months to fit its internal systems at Rosyth and it will be 2019 before the ship can begin sea trials.
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