The production had been due to run through until March 28.
A statement said: "Whilst we have no reason to disagree with current scientific and government advice on coping with the Coronavirus, given the new travel and other restrictions in place it is nevertheless becoming increasingly impractical to sustain business as usual at our theatre.
"We are very sympathetic to people’s personal circumstances, as we are to the audiences who are still excited to visit the theatre and see our productions. We are also extremely aware of our employees’ financial dependence on work being presented and tickets being purchased.
"So it is with great sadness that we have had to decide to suspend the presentation of Endgame in a double bill with Rough for Theatre II for the next two weeks, which is the remainder of its run."
Other productions at The Old Vic are currently going ahead as scheduled.
The Old Vic has offered refunds or credit for ticket holders but asked them to instead donate their ticket price in return for a video recording of Endgame, captured earlier in the run, a private video message of appreciation from the cast, and a free Friends membership including Priority Booking valid for one year.
Samuel Beckett’s Endgame was presented in a double bill with his rarely seen short play Rough for Theatre II.
Daniel Radcliffe starred in the cast as as Clov with Alan Cumming as Hamm. They were joined on the cast by Jane Horrocks as Nell and Karl Johnson as Nagg.
It follows The Turbine Theatre cancelling all of its performances through until at least April 16.
However most other theatres in London are currently open as normal at the time of writing.
Meanwhile, over in New York, Broadway is currently dark.
All productions were cancelled on March 12 for at least four weeks until April 13.