Johnson, who had been isolating in Downing Street after testing positive for the virus last month, was taken to hospital on Sunday night because he still had a high temperature and his doctors felt he needed additional tests.
His office and ministers said Johnson, 55, continued to run the government, that the prime minister was doing well and that he would undergo "routine tests" as a precaution, though Downing Street declined to say which tests he would have.
"He'll stay in hospital as long as he needs to do that, but I've heard that he's doing well and I very much look forward to him being back in Number 10 as soon as possible," Housing Secretary Robert Jenrick said.
"This isn't an emergency admission and so I certainly expect that he'll be back at Number 10 shortly," he said, though he gave no time frame.
On March 27, Johnson became the first leader of a major power to announce that he had tested positive. The 55-year-old went into isolation at an apartment in Downing Street.
It was not clear how an ill prime minister could lead the government's emergency response to the outbreak from a hospital. Some medics told Reuters it was unclear what was meant by precautionary tests for COVID-19 complications.
With only an unwieldy collection of sometimes ancient and contradictory precedents to go by, there is no formal succession plan should the prime minister become incapacitated.
Foreign Secretary Dominic Raab chaired the government's emergency COVID-19 meeting on Monday.
US President Donald Trump said Johnson was a "strong man" as he passed on his nation's best wishes.
"All Americans are praying for him," Trump told a news conference. "He's a friend of mine, he's a great gentleman and a great leader, and as you know he went to the hospital today but I'm hopeful and sure that he's going to be fine."
The pound fell against the dollar on news of Johnson's admission to hospital, announced just after Queen Elizabeth delivered a rallying call on Sunday night to Britons. It rose when Jenrick said he expected him to be back at Downing Street shortly.
Doctors said a person of Johnson's age with COVID-19 symptoms after 10 days was likely to be assessed for their oxygen levels, lung, liver and kidney functions, and undergo an electrocardiogram heart check.
"Clearly the prime minister is finding it difficult to shake this thing off," said Jonathan Ball, Professor of Molecular Virology at Nottingham University.
"What it does show is how difficult it is to predict how this infection will develop, and whilst most people will experience nothing more than an annoying cold, for others this can develop into a serious and sometimes life-threatening disease."
Medics said that patients with COVID-19 can deteriorate after about 10 days, with some developing pneumonia.
Johnson, who is not a smoker, said earlier this year that he wanted to lose weight.
Health officials said on Sunday the British death toll from the coronavirus had risen by 621 to 4,934.
PM IN HOSPITAL
Johnson, the face of the 2016 Brexit campaign, won a resounding election victory in December before leading the United Kingdom out of the European Union on Jan. 31.
He has faced criticism for initially approving a much more modest response to the novel coronavirus outbreak than other European leaders, saying on March 3 that he had been shaking hands with coronavirus patients.
He changed tack when scientific projections showed a quarter of a million people could die in the United Kingdom.
Johnson effectively shuttered the world's fifth-largest economy, advising people to stay at home and the elderly or infirm to isolate themselves for weeks.
The virus, though, had already penetrated the British government.
Johnson and his health minister tested positive last month and his chief medical adviser also self-isolated. Johnson's pregnant 32-year-old fiancée, Carrie Symonds, also had symptoms but said on Saturday she was feeling better.
From an apartment above Number 11 Downing Street, and with food brought to his door, Johnson continued to lead the government's response and chaired meetings via video conference.He has posted a series of video messages since then, initially appearing in a suit and tie but in the latest post on Friday, he appeared weary, sitting in a chair with his shirt open at the neck.