Ian Rapoport of NFL Network reported the news.
Robinson went down in Sunday's win over the Atlanta Falcons. He did not record a defensive stat in the game.
A 2010 first-round pick of the Saints, Robinson returned to the franchise this offseason after bouncing around to three teams in three years. He played the 2017 season with the Philadelphia Eagles, recording 47 tackles and four interceptions as part of the Super Bowl-winning defense.
The 31-year-old was an integral part of the Saints' defensive plan, serving as the third corner behind Ken Crawley and Marshon Lattimore. P.J. Williams and Justin Hardee will take more snaps with Robinson out of the lineup.
The Saints will also look to the open market or their practice squad for a replacement. Robinson's injury leaves them with only four cornerbacks on their roster at the moment.
New Orleans' pass defense has been the worst in football all season. The Saints are giving up an NFL-worst 11.2 yards per attempt and have picked off only one pass against 10 interceptions. Opposing quarterbacks have an astounding 141.7 rating against their secondary.