The Saints said that Grant, who anchored the left side of the Saints line, has a triceps injury that will end the season for the eight-year veteran. Grant had surgery to repair the torn muscle, the Saints said on Tuesday.
Grant, one of the few starters the Saints did not rest during the final game of the season, was hurt in New Orleans' 23-10 loss to the Carolina Panthers. He missed the last eight games of last season with a similar injury.
The 31-year-old Grant started every game this year and was credited with 53 tackles, 5½ sacks and a forced fumble.
In a related transaction, the Saints re-signed veteran defensive end Paul Spicer.
Spicer is a 10-year NFL veteran who first joined the Saints as a free agent last spring and played in all four preseason games before being released in the final preseason cutdown.
New Orleans (13-3) has a first-round bye in the playoffs. The Saints lost the last three games of the season, including an overtime defeat at home to the Tampa Bay Buccaneers. By the end of the regular season, the defense had slipped from the top 10 to No. 25 in yards allowed, the lowest ranking of any of the 12 playoff teams.
Although several starters rested in the meaningless loss to Carolina on Sunday, the defense gave up 1,725 yards in the previous four games, an average of 431.2 per contest. The Detroit Lions, who finished last in the NFL in total defense for the season, allowed 392.1.
Injuries have contributed to the defense's decline, but with the rest the bye week provides, the Saints hoped all 11 starters would be healthy for the playoffs.
Coach Sean Payton gave the Saints nearly a week off to clear their heads before they return to practice for double sessions Saturday and Sunday to begin preparing for a divisional playoff game.
New Orleans will open on Jan. 16 in the Louisiana Superdome against the Philadelphia Eagles, Green Bay Packers or Arizona Cardinals, depending on this weekend's first-round results.