The ban was reportedly instituted so that no photos of Witherspoon or Jake Gyllenhaal get out during filming, US Weekly reported Wednesday.
"Reese doesn't want any rumors about her and Jake," a source in Los Angeles told US, adding that security on the film is very strict.
Other sources report it was not Witherspoon who instituted the cell phone ban, but the studio, New Line Cinema.
Boston schools pull out free condoms over wrapping complaints
NBC reportedly holds celebs hostage to Jimmy Fallon's show