The aircraft carrier is about a quarter of the way through a 28-week deployment leading the CSG, which includes two Type 45 destroyers, two Type 23 frigates, two Royal Fleet Auxiliary ships, a US destroyer and 10 Marine Corps F-35B fighters, and is currently in the Indo-Pacific.
A Royal Navy spokesman said in a statement: "As part of routine testing, a small number of crew from the Carrier Strike Group have tested positive for COVID-19.
"All personnel deployed in the UK CSG have received both doses of the COVID vaccine and there are a number of mitigation measures on board including masks, social distancing and a track and trace system.
"The Carrier Strike Group will continue to deliver their operational tasks and there are no effects on the deployment."
All ships deployed on the mission recently stopped off in ports, including HMS Queen Elizabeth which docked in Limassol, Cyprus, with crew members getting the chance to take some shore leave.
American destroyer USS The Sullivans, which is part of the group, also stopped in Cyprus alongside HMS Queen Elizabeth.
While in Limassol, the ship's Captain, Commander David Burkett, was asked by Forces News whether COVID-19 had impacted operations at that time.
He said: "I think a lot about COVID, and I think a lot about how it impacts every single person on the ship. And I think a lot about service.
"We are all here to serve. You don't ask for the challenges that come your way. No more than the Sullivan brothers asked for war in WWII and the challenges they faced on the Juno.
"It is our job to overcome those challenges, they may not be what we asked for and they may not be what we want but that's our job.
"There was never a thought of postponing, there was only the thought 'how do we make this work and how do we make this work as effectively as we possibly can with what we have'."
The outbreak comes after Defence Secretary Ben Wallace on Tuesday pointed to the deployment as an example of the way UK and US militaries were able to operate "seamlessly" together.
Also on Tuesday, the Ministry of Defence confirmed an investigation was under way after a sailor died on board Type 23 frigate HMS Kent, also part of the CSG.
Cover image: HMS Queen Elizabeth leads other vessels from the Carrier Strike Group through the Suez Canal last week (Picture: MOD).