Wright, who missed the final seven games of the 2010 season after sustaining a concussion, suffered a second concussion in a season-opening win in Miami.
He returned to practice last week and engaged in two days of limited participation, but Thursday's move ends his season and could threaten his career. He registered a tackle and a half-sack against the Dolphins, his only appearance this year.
"Mike did everything he could to return and contribute to the team," said Patriots coach Bill Belichick. "Unfortunately, we felt the best course of action was to place him on injured reserve at this time."
Wright has 174 tackles and 15 sacks in 81 games with the Patriots. Undrafted out of Cincinnati, he played 13 games as a rookie before an ankle injury ended his 2005 season, and a foot injury ended his 2007 campaign after nine games.
He's been placed on injured reserve in four of his seven seasons with the team.
Adams signed with the Patriots on Sept. 21 and was active for games against Buffalo and Oakland, appearing on one special-teams play against the Raiders.
He originally was taken by the San Francisco 49ers in the seventh round (No. 224 overall) of the 2010 draft. Adams played in 15 games for the 49ers last season and finished with 13 total tackles and one pass defended.
Chris Forsberg covers the Patriots and Celtics for ESPNBoston.com.