Warner Bros confirmed filming had been suspended just days after it resumed because a member of the production team had tested positive for the virus but did not say who.
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.”
US outlets Variety and Vanity Fair quoted unnamed sources close to the production which said the person in question was the British actor.
The superhero film only recently returned to filming near London following a six-month hiatus due to the pandemic.
It was initially due for release in June 2021 but has been delayed until October 1 2021.
Directed by Matt Reeves, The Batman will Robert follow in the footsteps of Christian Bale, Ben Affleck, Val Kilmer, Michael Keaton and George Clooney in playing the Dark Knight.
The film also stars Zoe Kravitz as Catwoman, Andy Serkis as Alfred Pennyworth and Jeffrey Wright as Gotham City’s police chief Commissioner Gordon.
Last month, a trailer saw the Twilight star debut as a darker, brooding Bruce Wayne.
Fans also caught a glimpse of Colin Farrell in heavy prosthetics for his role as Penguin.
Representatives for Robert Pattinson have been contacted for comment by HuffPost UK.