The wedding of her granddaughter Princess Beatrice has been cut from the calendar, as well as her beloved Chelsea Flower Show, the Derby and Royal Ascot.
The Queen's Birthday Honours list that was due next month is also to be postponed.
Morton said: "It's terribly sad but I can't see how the Queen can resume her usual job.
"The Covid-19 virus isn't going away soon and will be with us for months, if not years. It would be far too risky for the Queen to start meeting people regularly.
"She has always loved getting out and meeting people but she can't take the risk.
"How can she carry out investitures, meet ambassadors, do walkabouts and visit places without meeting people at close range?
"If she gets the bug, it could be fatal and would put Prince Philip at risk."
He continued: "Prince Charles is, of course, over 70 himself but he has had the virus and probably has immunity now.
"The Queen's speech last month was brilliant and it brought the country together. To quote Churchill, it was her finest hour, but from now on we are maybe only going to be seeing her on video links.
"The Queen's address on Friday was inspirational because she served during the war and she lifted spirits because she has authority from her lifetime of experiences."