The Welsh government has announced plans to close its schools from Friday amid the outbreak.
Schools in Scotland will also shut their doors to pupils later this week, Nicola Sturgeon has said.
It comes as Boris Johnson is facing increasing calls to close the schools in England.
The prime minister has said further decisions on closures were "to be taken imminently".
Welsh minister for education Kirsty Williams said plans were being made for schools in Wales to be repurposed to help people "involved in the immediate response” to the outbreak.
She said: "I can announce we are bringing forward the Easter break for schools in Wales. Schools across Wales will close for statutory provision of education at the latest on 20 March 2020.
"I have been clear up to now that the continuity of education and the wellbeing of our learners has been at the heart of my decision-making. This will always be the case.”
Shortly after the announcement from the Welsh government, Ms Sturgeon said Scottish schools have now lost too many staff to continue as normal and will close by the end of the week.
Northern Ireland's education minister said he could not give a date for when schools will be closed.
Peter Weir said that when schools close over coronavirus, it will not be short term, but potentially until the end of August.
Jersey’s education minister has also made the decision to close the majority of schools and colleges to students from Monday.
It comes after education unions warned that keeping schools open is becoming "increasingly untenable" as staff are self-isolating.
On the Welsh government's decision to close schools, Laura Doel, director of school leaders’ union NAHT Cymru, said: “School leaders and teachers will want to be part of the national response.
“Schools play a pivotal role as part of the social fabric of our communities and we will work with Welsh government to make sure the support systems are in place to ensure key workers can remain in work.”
Eithne Hughes, director of the Association of School and College Leaders (ASCL) Cymru, added: “This is the right decision at the right time given the seriousness of the situation and the pressure on schools as staff increasingly self-isolate.”
She added: “We await a decision on this summer’s GCSEs and A-levels and continue to press for an announcement as a matter of urgency.”
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