The senior royals were all last together earlier this month.
Prince Charles and Camilla, whose test for the virus was negative, are now self-isolating in Scotland.
“Both of them remain in good spirits,” a palace source told PEOPLE.
“There is a sense of keeping calm and carrying on. The duchess is concerned for him but she is aware of his own good spirits and therefore is keeping a close eye on him and mindful of her own situation. She is upbeat.”
An insider told Daily Mail that Meghan's travel ban kicked in during the coronavirus outbreak, with the Duchess telling her husband that "under no circumstances, is she okay with him travelling anywhere right now."
The source added: "Meghan said Harry's been in touch with his dad... Of course, he's frustrated. She said they both are frustrated because they are doers and want to do so much more to help."
Prince Charles, 71, tested positive for the virus on Tuesday.
"The Prince of Wales has tested positive for Coronavirus," Clarence House confirmed on March 25.
"He has been displaying mild symptoms but otherwise remains in good health and has been working from home throughout the last few days as usual. In accordance with Government and medical advice, the Prince and the Duchess are now self-isolating at home in Scotland."His wife Camilla, 72, tested negative for the virus.
"The tests were carried out by the NHS in Aberdeenshire where they met the criteria required for testing."
According to The Mirror, "It is not possible to ascertain from whom the Prince caught the virus owing to the high number of engagements he carried out in his public role during recent weeks."
The shock diagnosis comes after Queen Elizabeth II fled to Windsor Castle to self isolate.
Royal insiders have claimed it's likely Elizabeth will stay in Windsor while the country is in the grip of the coronavirus pandemic.
A palace spokesman said: "As a sensible precaution and for practical reasons in the current circumstances, a number of changes are being made to The Queen’s diary.
"In consultation with the Medical Household and Government, a number of public events with large numbers of people due to have been attended by The Queen, and other Members of the Royal Family, in the coming months will be cancelled or postponed," the spokesman said.