The Prime Minister, 55, was moved on the advice of his doctors and is said to be receiving "excellent" care.
He is understood to be conscious and was moved to the ICU at about 7pm on Monday as a precaution should he require ventilation to aid his recovery.
Mr Johnson was admitted to St Thomas' Hospital in Westminster on Sunday for tests and observation after his coronavirus symptoms persisted for 10 days.
Foreign Secretary Dominic Raab will “deputise where necessary” while he is in intensive care, a No 10 spokesman said.
The spokesman added: “Since Sunday evening, the Prime Minister has been under the care of doctors at St Thomas’ Hospital, in London, after being admitted with persistent symptoms of coronavirus.
“Over the course of this afternoon, the condition of the Prime Minister has worsened and, on the advice of his medical team, he has been moved to the intensive care unit at the hospital.
“The PM has asked Foreign Secretary Dominic Raab, who is the First Secretary of State, to deputise for him where necessary.
“The PM is receiving excellent care, and thanks all NHS staff for their hard work and dedication.”
The Queen has been kept informed by Downing Street about his condition, Buckingham Palace said.
World leaders including US president Donald Trump, who described Mr Johnson as a "great friend", and France's Emmanuel Macron have voiced their support.
Mr Raab confirmed it was over the course of Monday afternoon that the PM’s conditioned deteriorated.
He said: “During the course of this afternoon, the Prime Minister’s condition worsened and, on the advice of the medical team, he’s moved to a critical care unit.
“So in light of those circumstances, the Prime Minister asked me as First Secretary to deputise for him where necessary in driving forward the Government’s plans to defeat coronavirus.
“And, as you’ll know, he’s been receiving excellent care at St Thomas’s hospital, and we’d like to take this opportunity as a Government to thank NHS staff up and down the country for all of their dedication, hard work and commitment in treating everyone who’s been affected by this awful virus.”
He added the Government was focused on “making sure we can defeat coronavirus”.
He said: “There’s an incredibly strong team spirit behind the Prime Minister, and making sure that we get all of the plans the Prime Minister’s instructed us to deliver, to get them implemented as soon as possible."
Health Secretary Matt Hancock, who has recovered after also contracting the virus, tweeted: "Sending all possible best wishes to @BorisJohnson and his loved ones. I know he will receive the best possible care from our amazing NHS."
Sending all possible best wishes to @BorisJohnson and his loved ones. I know he will receive the best possible care from our amazing NHS.— Matt Hancock (@MattHancock)April 6, 2020
Chancellor Rishi Sunak wrote: “My thoughts tonight are with @BorisJohnson and @carriesymonds. I know he’ll be getting the best care possible and will come out of this even stronger.”
— rishisunak (@RishiSunak)April 6, 2020
Home Secretary Priti Patel said: "My love & thoughts are with @BorisJohnson, @carriesymonds & the Prime Ministers [sic] family."
— Priti Patel #StayHomeSaveLives (@patel4witham)April 6, 2020
Jeremy Hunt, who ran against Mr Johnson in last year's Tory leadership race, added: "Keeping fighting Boris. Whole country behind you."
Keeping fighting Boris. Whole country behind you #BackBoris— Jeremy Hunt (@Jeremy_Hunt)April 6, 2020
Former Tory prime ministers David Cameron and Theresa May also tweeted their support.
— David Cameron (@David_Cameron)April 6, 2020
My thoughts and prayers are with @BorisJohnson and his family as he continues to receive treatment in hospital.
This horrific virus does not discriminate. Anyone can get it. Anyone can spread it. Please #StayHomeSaveLives— Theresa May (@theresa_may)April 6, 2020
Labour leader Sir Keir Starmer posted: “Terribly sad news. All the country’s thoughts are with the Prime Minister and his family during this incredibly difficult time.”
Ex-Labour leader Jeremy Corbyn added: "My thoughts are with Boris Johnson and his family tonight. Thanks to the #NHS staff for their hard work and dedication."
My thoughts are with Boris Johnson and his family tonight.
Thanks to the #NHS staff for their hard work and dedication.— Jeremy Corbyn (@jeremycorbyn)April 6, 2020
Scotland First Minister Nicola Sturgeon tweeted: “My thoughts are with the PM and his family – sending him every good wish.”
Mayor of London Sadiq Khan said: “Praying for the Prime Minister’s swift recovery tonight. @GSTTnhs has some of the finest medical staff in the world, and he couldn’t be in safer hands.”
Two uniformed police officers were stationed at the entrance to the hospital on Monday evening.
Throughout the day officers and police vehicles could be seen entering and exiting the central London hospital.
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The news came just a few hours after Mr Raab told a press briefing that the PM remained in charge of the Government despite still being under observation.