A traditional timetable for recovery from the injury is two to four weeks, with the Buccaneers re-signing linebacker Kevin Minter as a precaution on Tuesday. Tampa Bay (3-6) travels to MetLife Stadium to face the Giants (2-7) on Sunday (1 p.m. ET).
David was injured early in the third quarter of Sunday's contest while recording a tackle on Washington Redskins wide receiver Maurice Harris. The 28-year-old David was able to finish the contest.
The Buccaneers have been decimated by injuries at the linebacker position, namely with Kwon Alexander sustaining a torn ACL in Week 7. Kendell Beckwith broke his ankle in an offseason car accident while reserve Jack Cichy is also out for the season with an ACL tear.
David has collected a team-leading 71 tackles in nine games this season and is tied for a club-best nine tackles for a loss.
The 6-foot-1, 233-pound David has missed just five games in his 100-game NFL career that spans seven years.
David has recorded 836 tackles, 18.5 sacks, 18 forced fumbles and 12 fumble recoveries since being selected by the Buccaneers in the second round of the 2012 NFL Draft.