Downing Street said he was transferred to the unit on the advice of his physician team and received “excellent care.”
Mr Johnson has asked Foreign Secretary Dominic Robb to resign “where needed”, a spokesman said.
The 7-year-old PM was admitted to St. Thomas Hospital on Sunday evening with “regular symptoms”.
Buckingham Palace said the queen was notified about the health of Mr Johnson at No. 10.
World leaders, including US President Donald Trump and French President Emmanuel Macron, have expressed support for Mr Johnson.
BBC political correspondent Chris Masson said the prime minister was given oxygen on Monday afternoon before intensive care.
He was transported as a precaution so he could be closer to a ventilator – which undergoes a body-breathing process, our correspondent said.