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."
Vanity Fair said British actor Pattinson, 34, caught the virus days after shooting resumed near London, after a six-month delay to filming.
The Batman was initially due for release in June 2021 but has been delayed to October 2021.
In the latest film, directed by Matt Reeves, Twilight star Pattinson follows in the footsteps of Christian Bale, Ben Affleck, Michael Keaton and George Clooney in playing the Gotham City superhero.
Pattinson, who also co-stars in the current cinema hit Tenet, has not commented on the reports.