The Saints, in moves made Tuesday, also have placed receiver Marques Colston, safety Jairus Byrd and defensive lineman Glenn Foster on the physically unable to perform list. Those three players remain on the active roster and could return to the field at any time during the preseason.
Bunkley spent three seasons in New Orleans, starting all but two of 38 games in which he played. He hasn't had a sack since 2012, but with his 6-foot-2, 306-pound frame he was often effective holding his position at the line of scrimmage and occupying blockers.
The Saints hold their first practice of training camp Thursday.
Bunkley, 31, suffered a season-ending quadriceps injury last November. But the Saints recommitted to him in March by agreeing to a reduced contract that included a $250,000 roster bonus.
It's unclear if Bunkley was dealing with a new injury this summer, but he did not participate in OTAs or minicamp.
John Jenkins, a third-year nose tackle who was expected to push Bunkley for his starting job even before the release, should step into that role as the primary run stuffer in the Saints' base defense.
The Saints have now replaced four starters from last year's 31st-ranked defense after also releasing embattled linebacker Junior Galette on Monday.
Information from The Associated Press and ESPN's Mike Triplett was used in this report.