The number of EastEnders episodes screened will also be cut from four to two per week, the broadcaster said.That will allow it to make the existing recorded episodes last for "as long as possible."
A BBC spokesperson said "In light of the spread of Covid-19, after much consideration, it has been decided that filming on EastEnders will be postponed until further notice.
"We will continue to follow the latest news and advice from the World Health Organisation and Public Health England."
Meanwhile, ITV said Coronation Street would keep filming on a reduced schedule and would go down to three episodes a week.
Earlier in the week, the BBC announced that news programmes including Politics Live and Victoria Derbyshire had been temporarily suspended, allowing its news channel to focus on "core news".