Onward is one of the titles that has been hit by the coronavirus outbreak Photo: Disney/Pixar
Although the announcement fell short of a ban, he said: "Now is the time to stop all non-essential contact with others."
He added: "You should avoid pubs, clubs and theatres and other such social venues."
At the moment, most of the cinemas in the UK remain open, although Showcase introduced "social distancing" measures at the weekend and the ICA in London has suspended operations.
Box office numbers have already been hit by the Covid-19 outbreak, which saw revenues from recent releases, including Onward and The invisible Man, slashed by around half.
It was announced earlier that all cinemas in New York City will close from tonight.