Sheila Oakes, the mayor of Heanor, made the inflammatory comments in response to a Facebook post asking people to “say a little prayer" for the prime minister on Monday evening.
Oakes commented underneath the social media post: "Sorry, he completely deserves this and he is one of the worst PMs we've ever had."
She has since apologised and accepted she "made a mistake" with the outburst.
"I didn't think what I said would upset so many people,” Oakes told BBC News, “It came across as not a nice thing to say.
"I'm concerned about nurses and doctors who don't have protective equipment. I said something when I was angry without thinking about the prime minister or his family."
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The Amber Valley Labour Group said it had withdrawn the whip over Oakes’ comments, meaning she is no longer a party councillor.
Chris Emmas-Williams, the leader of Amber Valley Labour group, confirmed there would be an investigation into Oakes' conduct.
He said: "This behaviour is totally unacceptable and not what the Labour Party are about.
"I've not made the comments but I feel as leader of the Labour group I have to apologise as well to Boris Johnson and his family and we wish him well because we need everyone possible to fight this disease."
Number 10 announced on Tuesday morning that Mr Johnson is “stable” after spending the night in intensive care following a worsening of his symptoms.
The prime minister’s official spokesman said he had been receiving “standard oxygen treatment” but had not required any other assistance in breathing.
Johnson was originally admitted to St Thomas’ on Sunday on the advice of his doctor after continuing to display symptoms of cough and high temperature 10 days after testing positive for the virus.
His spokesman said at the move was a “precautionary step” in case he needed to be put on a ventilator.
“The prime minister has been stable overnight and remains in good spirits,” the spokesman said.
“He is receiving standard oxygen treatment and breathing without any other assistance.
“He has not required mechanical ventilation or non-invasive respiratory support.”