Garrett added that back issues have plagued Crawford in the past but the issue has flared up again.
Starting all 16 games last season, Crawford registered 35 tackles and five sacks.
Crawford's injury is a harsh sting for the Cowboys in the wake of defensive end Demarcus Lawrence's four-game suspension for violating the NFL's substance-abuse policy and Randy Gregory's suspension for the same offense. Gregory, however, is facing an additional suspension and has enrolled into a treatment program.
The decimated Dallas D-line will also currently is without the services of defensive end Benson Mayowa, who had offseason knee surgery, and rookie defensive tackle Maliek Collins. Mayowa is expected to be back before training camp is over. Collins broke his foot during the last week of OTAs and is expected to miss camp.