Werth was hit by a pitch while batting on May 15. Nats manager Matt Williams says there's no timetable for his return.
Werth, in his fifth season with Washington, had the wrist examined at the Mayo Clinic.
This is the third time the 36-year-old has suffered a broken left wrist. In 2012, he missed 75 games after breaking the wrist while sliding to make a catch.
Werth said the most recent injury reminds him of the one he sustained in 2005 while playing for the Los Angeles Dodgers. He missed 44 games to begin the season after being injured on the final day of spring training.
Werth missed the entire 2006 season after undergoing surgery to repair ligaments in the wrist.