As a preview of the dialogue we'll be missing, Trump's campaign manager Bill Stepien, who has also tested positive for covid-19, called the Commission on Presidential Debates "swamp creatures", attacking them for rushing "to Biden's defence by unilaterally cancelling an in-person debate".
The Trump administration claimed the commission made the change in favour of Mr Biden.
"President Trump will have posted multiple negative tests prior to the debate, so there is no need for this unilateral declaration", Stepien said in a statement.
The Biden campaign welcomed the move from the debate commission.
Incumbent Vice President Mike Pence, Trump's Republican running mate, was set to square off with California Senator Kamala Harris, Biden's Democratic running mate, in the vice presidential debate on Wednesday, Oct. 7, in Salt Lake City. But Mr Biden's advisers rejected squaring off that late in the campaign.
But CPD Chairman Frank Fahrenkopf later said the decision to hold the debate virtually, guided by its medical advisers at the Cleveland Clinic, was not going to be reversed. It's quite possible Trump holds firm and backs out of doing next week's debate but that would be a massive mistake for him.
The Biden campaign initially said that Joe would be happy to take part in a virtual debate, but after learning of Trump's refusal to participate they released a second statement saying that Biden "will find an appropriate place to take questions from voters directly on October 15th, as he has done on several occasions in recent weeks". As he campaigned in Arizona, Mr Biden said he would indeed attend the October 22 debate, scheduled for Nashville, Tennessee.
"We agreed to three debates back in the summer", Mr Biden said. And if, in fact, he shows up, fine.
"I'm not going to do a virtual debate", he declared.
The Democratic candidate said earlier this week he did not think the debate should go on if Mr Trump still had COVID-19.
Mr Trump's doctor, Sean Conley, said the President has had no COVID-19 symptoms for more than 24 hours and has been fever-free for more than four days.
"The CPD and the media can not hide Joe Biden forever", the Trump campaign wrote.
A debate before an audience of tens of millions of television viewers could provide that reset. GOP strategists say the party's support began eroding after his seething performance against Mr Biden last week when he did not denounce a white supremacist group.