A Saints spokesman said Saturday that both players had been downgraded on the official injury report from questionable to out with knee injuries.
Bush and Ellis are expected to be back at practice next week.
The Saints also will be without their two top cornerbacks, Jabari Greer and Tracy Porter, because of injuries, but a league source told NFL Network's Jason La Canfora that free safety Darren Sharper is expected to play. Sharper sat out last Sunday's victory over the St. Louis Rams because of a knee injury.
Bush missed practice this week with swelling in his left knee, the same one on which he had surgery last December to repair cartilage. Bush is coming off one of his best games of the season last weekend, when he gained 98 yards and scored two touchdowns on six rushes and two receptions.
Bush has 484 yards and six touchdowns in combined rushing and receiving this season.
Ellis sprained his right knee in Week 7 at Miami and returned to practice this week on a limited basis. A first-round draft pick in 2008, Ellis is one of New Orleans' primary run-stuffers.
The Associated Press contributed to this report.