Hitchens suffered the injury with 19 seconds left in the first half of Saturday night's preseason game against the Oakland Raiders. He will undergo additional testing, but if the diagnosis confirms the Cowboys' fears, then he would likely miss the season and need surgery.
Asked if he knew whether Hitchens' injury was an ACL tear, Cowboys owner Jerry Jones said: "I don't want to go there. All I know, though, is I don't like the way it sounds. They'll take a look at it again tomorrow. If it were going to put him down, it'd be an ACL tear."
Hitchens started every game last year and was credited by the coaches with 104 tackles, 1.5 sacks, 4 tackles for loss, 5 quarterback pressures and 2 pass breakups.
If Hitchens is out for the year, the Cowboys could move Sean Lee to middle linebacker or go with Jaylon Smith, who missed his rookie season with a serious knee injury and has played less than 30 snaps so far in the preseason.
Damien Wilson, who starts at strongside linebacker and can play multiple spots, is facing a potential suspension for an offseason arrest.
Hitchens had at least 100 tackles in two of his first three seasons, starting 36 of 48 games.