Morgan missed last weekends win over Crewe through suspension, but picked up an injury in the loss to Coventry on New Years Day before he was sent off.
Boss Steve Evans confirmed: "He will be out for another two or three weeks as he's had a small piece of floating bone removed. It was a minor procedure so it's in the short term he'll be missing."
Morgan looks set to miss the home game with Crawley, and away trips to Tranmere and his former club Preston.
Meanwhile Addison, who made his debut in the Crewe victory after joining on loan from Bournemouth, has been passed fit after fears that a similar injury had been sustained on the training ground, but Evans confirmed that the player is only suffering from bruising.
The defender went for a scan yesterday as a precaution and is set to be included in Evans' squad for the trip to strugglers Shrewsbury.