The pause in filming, confirmed by Warner Bros, is because lead actor Robert Pattinson has tested positive for the virus, according to US media.
Warner Bros said a member of the production team was self-isolating but it did not say who.
Filming began in Glasgow earlier this year but was halted due to the pandemic.
A spokeswoman for the studios said: "A member of The Batman production has tested positive for Covid-19, and is isolating in accordance with established protocols. Filming is temporarily paused."