Prisons in England and Wales have been put on "immediate lockdown" with all visits cancelled.
The Ministry of Justice and Her Majesty's Prison and Probation Service said the measure was to "ensure the safe and secure functioning of our prisons, while enforcing social distancing."
It follows the Government's strengthening of stay-at-home measures, announced in an address to the nation by the Prime Minister on Monday night.
HMP Birmingham, HMP High Down, HMP Manchester, and HMP Oakwood all have one confirmed case of coronavirus.
The Prison Officers' Association (POA) said it "praised the decision [...] to place prisons in England and Wales on immediate lockdown".
According to the union, a series of additional restrictions inside jails will mean inmates generally being locked up - but allowed to access showers, phones and exercise - with social distancing restrictions in place.
The group also suggested the measures will allow prisoners who carry out kitchen, cleaning and laundry work to continue.
In a statement, the POA also claimed prisoners due at court "will be discharged to attend unless the courts service advise us otherwise".
On Monday, it was announced that all jury trials in England and Wales will be put on hold and no new trials will start as part of ongoing efforts to halt the spread of Covid-19.
Last week it was announced that no new jury trails would begin.
The Ministry of Justice has been contacted for comment.
Elsewhere, the University and College Union (UCU) has called for face-to face prison education to be suspended - raising concerns about workers' safety.
A small-scale poll conducted by the union found that 63% of prison education staff said hand washing facilities are inadequate at facilities.
UCU general secretary Jo Grady said: "Education has a vital role to play in prisons, but we must ensure the safety of staff and prisoners first and foremost, and do everything possible to limit the spread of the coronavirus.
She added: "We want to work with the prison service to look at ways to get alternative learning materials to prisoners, but the face-to-face teaching must end for now."
The gov.uk website on coronavirus guidance for prisons states: "Handwashing facilities are available to prisoners, staff and visitors and we have worked closely with suppliers to ensure the supply of soap and cleaning materials".
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