All sailings due to start before those dates have now been axed.
Cunard will be contacting guests and travel agents who are impacted.
All guests who have had their voyage cancelled will automatically receive an enhanced 125 percent Future Cruise Credit.
Alternatively, they can fill in the website form for a 100 percent refund.
Cunard president Simon Palethorpe said: “We are so sorry to all those guests who were due to sail on any of the cancelled voyages and for the disappointment this news will cause.
“After very careful consideration and reviewing the latest guidance, we simply do not feel it would be sensible to start sailing again with our current schedule so we have reviewed future itineraries.
“Queen Elizabeth has returned to the UK and with ongoing uncertainty over the re-opening of many ports and countries, it is sadly not practical to continue her planned itineraries for 2021.
“Therefore, in addition to the pause in operations, all of Queen Elizabeth’s sailings due to depart between March 26, 2021 and December 13, 2021, in and around Australia, Japan and Alaska, will be cancelled.”
Palethorpe continued: “These voyages will be replaced with a programme of shorter duration European holidays ranging from three to 14 nights, departing from Southampton.
“These will start at the end of March 2021, with a series of scenic voyages around the coast of Cornwall, the west coast of Ireland and the Scottish Isles.
“There will also be short breaks to Amsterdam which will include an overnight in the city, as well as voyages to northern and southern European destinations including Norway and the Iberian coast, with several of these itineraries featuring overnight city stays.
“Queen Elizabeth’s new programme will be completed with a series of seven and 14-night voyages in the Mediterranean, sailing from Barcelona.
“It is an exciting new programme which I am sure will have great appeal.”
All new itineraries onboard the Queen Elizabeth will be available to book from September 29, 2020.
Palethorpe added: “Additionally, recognising the immense disappointment of those on board Queen Mary 2’s curtailed World Voyage this year, and the cancellation of her World Voyage in 2021, we are delighted that Queen Mary 2 will sail a classic World Voyage in 2022.
“This will replace her scheduled sailings departing January 3, 2022 to April 3, 2022, including the voyage to South America.”
Full details of the changes to operations and options available to guests due to travel on cancelled voyages, as well as the latest updates, can be found at www.Cunard.com.