Speaking about school closures, he said: "This does mean that exams will not take place as planned in May and June but we will make sure that children do get exams and qualifications they need.
"For many parents this will be frustrating and it will make it harder for them to go out to work.
"That is why we are now working on further measures to ensure that we support not only businesses, but individuals and their families to keep the economy going.
"I also need to remind parents that children should not be left with grandparents or older relatives who are particularly vulnerable."
Schools in England will close until further notice for all pupils except children of key workers and the most vulnerable, Education Secretary Gavin Williamson said.
Williamson confirmed that assessments and examinations will not take place in the current academic year.
"We will work with the sector and Ofqual to ensure that children get the qualifications that they need.
"My department is working closely with local authorities, representatives of early years schools and headteachers, regional schools, commissioners and bodies such as Ofsted and Ofqual about how to deliver this change as effectively as possible.
"And we will do whatever is necessary to support local authorities, schools and teachers through the weeks and months ahead."
The Government has asked independent schools and boarding schools to close due to the coronavirus.
Johnson believes he also has the power to close private schools, but reassures churches that the Government is working to compensate them.
He said: "On schools, clearly the government will be closing the schools and we have the power to do that. When it comes to private schools I believe we have the same powers, obviously we will work to ensure that churches and so on are properly compensated."
When asked if there was intention to bring in legal restrictions on when or where people can travel around in London, Johnson responded:
"We live in a land of liberty as you know and its one of the great features of our lives that we don't tend to impose those kind of restrictions on people in this country.
"But I have to tell you we will rule nothing out, and we will certainly wish to consider bringing forward further and faster measures where that is necessary to suppress the peak of the epidemic to protect our NHS, to minimise casualties, and to minimise suffering."
Meanwhile, thousands of UK holidaymakers face a race against time to return home before countries around the world shut down due to the coronavirus.
Travellers in Morocco accused airlines of leaving them stranded and demanding extortionate fees.
Thomas Reilly, the British ambassador to Morocco, said "we are trying to get as many flights in as we can" before the country's airspace closes tomorrow.
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In response to a holidaymaker who sent him a Twitter message complaining that Ryanair was charging £300 for a flight back to the UK, he replied: "Buy the tickets. Get out of the country. Claim on your insurance. Do not delay."
The Foreign and Commonwealth Office (FCO) advised travellers in Spain to return home before March 24 as its Government has ordered all hotels to close from that date.
Dave Cook, 36, from Edinburgh, was stranded in Japan after his KLM flight home last week was cancelled. He told said he felt "left in the dark" by his travel firm lastminute.com and had bought a new flight for more than £1100.
"I'm a contractor so don't get holiday pay, so I had to err on the side of caution in case we couldn't get a flight for a while," he said.
Author Clare Josa, 46, of Sussex, is struggling to return to the UK from South Africa with her 12-year-old son. She said British Airways initially wanted £12,000 for them to switch to an earlier flight.
It later waived that fee, but there were no spare seats, forcing the pair to hope their flight is not among the many thousands being cancelled.
