According to Cunard, a "small number" of crew members had tested positive and the line had put in place "approved isolation protocols".
The company is due to restart ex-UK cruises after suspending all sailings in March 2020.
Cunard Line said:
"We have comprehensive health and wellbeing procedures in place to protect all on board, which have been developed with guidance from our global medical, public health and industry experts and in close coordination with Government departments."
~800 crew are currently on the ship.
Queen Elizabeth's next scheduled cruise to nowhere is to Cornwall, departing Southampton England on July 19. It is the first of these "staycation cruises" around the UK coast scheduled for the summer.
Currently, voyages around the British Isles are permitted. However, international cruises haven't been allowed to resume.
For more Queen Elizabeth accidents and incidents see the ship's CruiseMinus page.