Crocker has been bothered by a bad ankle for weeks but re-injured it Sunday and was carted off the field during a 30-10 loss to the Minnesota Vikings.
The Bengals (9-4) were hopeful Crocker could return in time for the postseason, the source said.
The Bengals travel to play the San Diego Chargers (10-3) on Sunday in a game that could determine the No. 2 seed in the AFC.
Backup Tom Nelson will fill in for Crocker, the second significant injury to Cincinnati's safety position this season.
Former starter Roy Williams was put on injured reserve in November with an arm injury.
James Walker covers the AFC North for ESPN.com.