The 280-metre warship, the biggest and most powerful ever built by Britain, is leaking because of an issue with a shaft seal, according to a Royal Navy spokesman.
He 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."
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The 65,000-tonne vessel, which has an estimated 50-year working life, is thought to have been leaking for some time.
About 10,000 people were involved in the construction of the aircraft carrier, which can travel in excess of 25 knots.
It was constructed in sections which were transported to Rosyth in Fife, and put together.
Shipbuilding yards Govan and Scotstoun in Glasgow, Cammell Laird in Liverpool, Appledore in Devon, as well as A&P on the Tyne in Newcastle, and Portsmouth were involved.
Theresa May hailed the ship as a symbol of a "great global maritime nation" after it arrived at its base in Portsmouth for the first time in August.
"Britain can be proud of this ship and what it represents," said the Prime Minister.