Galette experienced the injury in practice Wednesday and will have surgery to repair the tendon on Friday.
Galette signed with Washington July 31 after being released by New Orleans due to off-field issues. He was set to make his preseason debut Saturday against Baltimore after spending time rehabilitating a torn left pectoral muscle.
The 27-year-old linebacker recorded 45 tackles, 10 sacks and three forced fumbles last season with the Saints.
In January, Galette was arrested on misdemeanor domestic violence and battery charges. The charges were dropped in February and the woman in the case filed a civil lawsuit the same day. The status of the case is uncertain, as the woman's attorney is no longer representing her and no new attorney has taken the case.
Last month, the NFL said it was aware of a video posted in 2013 that appears to show Galette striking multiple people with a belt. Galette’s attorney has denied that Galette was the man shown in the video.
- Jeremy Woo