George Kerevan, who served as MP for East Lothian between 2015 and 2017, made the remarks after Clarence House revealed the Prince of Wales had tested positive for Covid-19.
Posting on his Twitter account to more than 16,000 followers, Mr Kerevan said: “This billionaire land owner disobeyed guidance to stay home to avoid spreading virus, went to second home in Scotland, is now infected and has infected others.
“Indy Scotland must be a republic and tax this arrogant fool.”
Speaking to The Herald, Scottish Conservative deputy chief whip Alexander Stewart said: “This is a classless and tasteless intervention from a former SNP MP who should know better.
“Most decent people will be wishing Prince Charles well in his recovery.
“Instead, Mr Kerevan is using the coronavirus to make political points about independence – it’s a complete disgrace.”
Social media replies
Underneath Mr Kerevan’s tweet, nearly 200 people commented on his remarks.
Many backed the journalist’s call for a republican Scotland in the event of independence.
But others agreed that his comments were in poor taste. Daniel Pizzaro tweeted: “What a horrible thing to say.”
Another user, Sandie Smith, responded: “Have you any idea how nasty you sound?”
First Minister responds
Nicola Sturgeon said: "I send my best wishes to Prince Charles."
Asked if he should have come to Scotland at all, she said: "I will repeat what I've said - we want people to behave responsibly and not see the Highlands and Islands as places where they can try to outrun the virus, that's not possible.
"Of course people have homes in Scotland and people will choose to go to their homes, but generally speaking remote areas are under pressure as health services are further away, and we don't want people putting more pressure on these services."
Chief Medical Officer Dr Catherine Calderwood said she had spoken to NHS Grampian and Prince Charles had been tested for "clinical reasons".
She added: "I'm pleased to say he's very well and like many who have had this virus, has had a mild illness."
A Clarence House spokesman said: "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.
"The Duchess of Cornwall has also been tested but does not have the virus. 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.
"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."
Impact on The Queen
Last week, The Scotsman reported that the Queen had left London for Windsor Castle to socially distance herself amid the coronavirus pandemic.
A statement from Buckingham Palace this morning read: “The Queen remains in good health. The Queen last saw The Prince of Wales briefly on the morning of March 12 and is following all the appropriate advice with regard to her welfare.
“We will not be commenting further.”
Her Majesty headed for the sanctuary of her Berkshire home a week earlier than she normally would at this time of year, and is expected to remain there beyond the Easter period.
Her Wednesday audience with the Prime Minister will, for the foreseeable future, take place on the phone.