The duchess is said to have ramped up her precautions against the virus in recent days, a close friend told DailyMail.com.
"Meghan said hearing the news of Prince Charles has put everyone on edge.
"She said she is worried about her own health and Harry's health because she doesn't want to pass anything onto Archie," the insider said.
According to the publication, the royals' staff members must all wear latex gloves to curb infections.
And now anyone who runs errands for the couple must wear a face mask at all times and staffers must leave their shoes and coats outside, the friend said.
They explained: "Meghan said she would rather be overly cautious than not."
Earlier this week, an insider told Daily Mail that Meghan's has banned Harry from travelling to the UK 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."
The Sussexes last saw Charles earlier this month before leaving for North America.
Prince Charles, 71, tested positive for the virus on Wednesday, and is is in self-isolation.
"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."
"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."
Prince Charles spoke out on Thursday after his shock diagnosis to thank fans for their messages of support.
"Thank you for all your ‘Get Well Soon’ messages for His Royal Highness. He is enormously touched by your kind words," the royals posted to the Clarence House Instagram account.