They replaced him on the roster with second-year cornerback Trevin Wade.
Greer suffered the nasty injury during the first quarter of Sunday's 23-20 victory over the San Francisco 49ers when he landed awkwardly after breaking up a pass.
The 10th-year veteran, who has been a full-time starter since he joined the Saints in 2009, was playing at a high level this season for a resurgent defense. He had one interception and 12 pass defenses (including two before he left Sunday's game).
Greer will likely be replaced in the starting lineup by second-year player Corey White, a physical corner who has shown promise in his young career. White immediately stepped up with an interception in the second quarter Sunday -- though he wound up fumbling the ball through the end zone for a touchback during his return.