The senior defensive end is scheduled for shoulder surgery and will miss the rest of the Hogs' season.
The injury to Wright comes just days after losing senior linebacker Alonzo Highsmith for the rest of the season to a foot injury in the first half of the Auburn game.
Smith is hopeful that Tevin Mitchel will be able to return at cornerback for the Hogs, which would allow them to shift some guys around in the secondary.
Another player the Hogs will see back is junior defensive end Chris Smith, who was arrested early Wednesday for failure to appear in court.
The Arkansas Razorbacks play the Kentucky Wildcats this Saturday.