Fletcher, 29, is a former third-round pick of the Rams back in 2009. He joined the Eagles as an unrestricted free agent back in 2013 before signing on with the Patriots this past March.
New England signed him to a one-year, $1.5 million contract, but he has been active for only two games this season.
According to OverTheCap.com, releasing Fletcher will free up $1,581,250 in available cap space while creating $550,000 in dead money.
This season, Fletcher has recorded 10 tackles and a forced fumble for the Patriots over the course of two games.