The Royal Navy warship had been expected to depart Portsmouth Naval Base for a period of sea training at the start of next week.
But a spokesman for the service confirmed that the departure would be delayed by 48 to 72 hours for the 700-strong crew to be tested.
He explained that once the ship had sailed, it would spend a period in quarantine to ensure all of the crew were clear of the virus.
The move comes after shadow defence secretary John Healey called for the military to be tested and for large-scale training exercises to be postponed to protect personnel.
His call comes after more than 600 members of the crew of a French aircraft carrier and accompanying vessels tested positive for coronavirus, while the US navy said a sailor who tested positive for Covid-19 on the USS Theodore Roosevelt has died.
The Navy spokesman said: ‘In addition to an isolation period at sea, the Royal Navy is now making use of spare NHS testing capacity to test the crew of HMS Queen Elizabeth prior to sailing. This will necessitate a short but manageable delay in sailing.
‘This is the right and sensible thing to do to ensure the Navy can continue to deliver on operations now and in the future.’
Defence secretary Ben Wallace told MPs on Wednesday that he had given all ships captains in the Royal Navy full authority to return to port, come alongside or evacuate if they had an outbreak on board.
He said: ‘I have spoken to the captain directly myself and said we will not judge you, we will not think any the worse of you if when you are at sea you feel the need to come back because of a crew outbreak.
‘I have also said to the First Sea Lord, you must justify in writing why it is necessary to put to sea."
He added of the carrier: ‘It is going to be in UK waters so it is not very far away - it's going to be within helicopter distance if we need to send someone back.
‘I think that plus well-worn traditional isolating rules which ships have always had to do, I think puts us in a place where we look after the welfare but maintain the defence operations that we have to do.’
The Queen Elizabeth is due to sail for a period of sea training and carrier training around the UK to help prepare it to be in a position to declare carrier strike capability later this year ahead of its first deployment planned for early 2021.
The spokesman added: ‘HMS Queen Elizabeth is sailing to conduct operational sea training, required as preparation for further training later this year and which together will ensure that she is ready for deployment in 2021.
‘The continuation of this training has been agreed by senior leaders across defence.
‘She will be operating in waters close to the UK coast and the commanding officer has discretion to cease the training, if deemed necessary.’