The 28-year-old Crabtree, who has played three seasons with Green Bay and one season with Tampa Bay, signed on Tuesday. In a corresponding move, the Saints placed injured safety Jairus Byrd on injured reserve.
The Saints have not discussed the severity of Graham's left shoulder injury, which occurred in the first quarter of last Sunday's victory over Tampa Bay.
The Saints have a bye this week and are not required to list Graham on an injury report until Oct. 15.
Crabtree had his best season with the Packers in 2012, when he caught eight passes for 203 yards and three touchdowns.
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