The PM was taken to a London hospital on Sunday evening with "persistent symptoms" - including a temperature - for a series of routine tests.
It is said to be a "precautionary step" taken on the advice of his doctor.
Mr Johnson, 55, tested positive for coronavirus 10 days ago.
Foreign Secretary Dominic Raab will chair Monday morning's coronavirus meeting in his place, Mr Jenrick said.
Last month, the prime minister's spokesman said if Mr Johnson was unwell and unable to work, Mr Raab, as the first secretary of state, would stand in.
Mr Jenrick told BBC Breakfast: "We hope that as a result of these tests [the prime minister] will be able to come back to Downing Street as soon as possible.
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