The warship was only accepted into the Royal Navy fleet by The Queen earlier this month.
At 280m long and with an estimated half-a-century working life, the behemoth is the biggest and most powerful ever built by the UK.
It is understood the vessel has been leaking for some time.
A Royal 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.”
The aircraft carrier weighs 65,000 tonnes and has a top speed in excess of 25 knots.
A number of ship-building yards around the country were involved in the build - these include Govan and Scotstoun in Glasgow, Appledore in Devon, Cammell Laird in Liverpool, A&P on the Tyne in Newcastle and Portsmouth.
Around 10,000 people worked on construction of the ship, made up in sections at yards around the UK and transported to Rosyth, Fife, where it was assembled.
Captain Jerry Kyd spoke to the Press Association ahead of the ship’s commissioning earlier this month, describing it as a “major milestone”.
The ship’s commanding officer said: “Building aircraft carriers is not for the fainthearted. There are very few countries who can do this around the world.”
He later added: “Putting together an aircraft carrier and all its facets and all its bits and pieces is quite a complicated business, (but) one we are looking forward to.
“This (the commissioning) is a major milestone now, it is all systems go really.”