The studio did not name the person infected or indicate when filming would resume.
Vanity Fair magazine, however, said it had confirmed through "highly placed sources" that 34-year-old Pattinson was the sick cast member.
Pattinson's representative could not be immediately reached for comment.
Production for the new film -- a dark, detective-style mystery take on the "Caped Crusader" -- also had to shut down midway through production in March due to the Covid-19 pandemic.
Director Matt Reeves has said his version -- due out next June -- is inspired by classic films noirs like "Chinatown" and "Taxi Driver," and will meet a "very human and very flawed" Bruce Wayne in his second year as Batman, trying to solve a series of crimes.
First-ever footage from the much-hyped movie released at the DC FanDome event last month left fans drooling online, with a mysterious villain leaving notes for Batman at crime scenes across Gotham -- and the film's hero pummeling a street thug before growling: "I'm vengeance."