All 91 of the company's cinemas will close from Tuesday 17 until further notice, in line with the Government's advice on the Covid-19 outbreak.
Boris Johnson has called on people to stay away from pubs, clubs and theatres and to avoid all non-essential contacts and travel.
Major chains including Odeon, Cineworld and Picturehouse had already announced plans to close their doors for the foreseeable future.
Tim Richards, founder and chief executive of Vue International, said: "Since the first news of the Covid-19 outbreak, we have been doing everything we can to provide a high-quality, enjoyable and safe big-screen experience for our customers.
"However, in line with the UK Government's latest public health advice we will be closing all our 91 cinemas in the UK & Ireland from today, March 17, until further notice.
"As you would expect, we are also doing our part by putting employment policies in place so that our staff are protected and are not penalised financially.
"We want to wish all our customers and employees well during these difficult times. Thank you for your continued support and we look forward to welcoming you back at one of our cinemas soon."
Earlier today, Cineworld and Picturehouse said they were shutting all UK outlets starting from Wednesday 18 while outlets in Ireland will close on Tuesday 17.
Cineworld Group chief executive Mooky Greidinger said: "At Cineworld and Picturehouse, we are committed to providing safe and healthy environments for our employees and guests and have therefore made the difficult decision to close our cinemas in UK and Ireland until further notice.
"We deeply value our cinema-loving customers and have no doubt we will be serving everyone again as soon as possible with a full slate of Hollywood blockbusters and the best of independent films and content."
In a report addressing the Covid-19 outbreak, the Everyman Media Group addressed the impact on its cinemas.
It said: "Trading over recent days has been impacted by Covid-19 and the delay of major movie releases. Following guidance provided by the UK Government yesterday, the board of Everyman has taken the decision to close its venues to guests until further notice. The health of our staff and our customers is the board's highest priority."
The report said it had begun cost-management measures including "the postponement of new sites, refurbishments and other capital expenditure projects".
It said Everyman had "significant headroom in its loan facility and is in dialogue with its lenders on covenants to maintain liquidity through this period of uncertainty".
The BFI Southbank, the screening complex operated by the British Film Institute, said it was closing "effective immediately".
A tweet said: "It's with great regret that, due to the rapidly evolving Covid-19 pandemic, and following Government's updated advice, we've taken the decision to close BFI Southbank effective immediately.
"All forthcoming events & screenings are now cancelled or postponed."
The move comes after theatres in the West End and around the UK closed on Monday as part of stringent measures aimed at tackling the spread of coronavirus.
The Society Of London Theatre - which represents hundreds of theatres in the capital including the National Theatre, London Palladium and London Coliseum - and UK Theatre said the decision was "not taken lightly".
The Royal Shakespeare Company also announced its three theatres will close following the Government's advice.