Hassen suffered a head injury in their 1-0 defeat to Senegal during the semi-finals, although he managed to complete the duration of the match.
The Nice shot-stopper featured in all but one of the Carthage Eagles games in the tournament, missing their opening match against Angola, where they played out a 1-1 draw.
After returning to the side, 24-year-old helped his side keep two clean sheets in the competition.
Msakni, meanwhile, was forced off in the 46th minute against the Teranga Lions due to a muscle strain and was replaced by Naim Sliti.
The Eupen forward has been a consistent performer for the Carthage Eagles prior to the injury, featuring in all their games in the tournament and scoring twice.
Msakni is the only player involved in at least one goal in each of the last six Africa Cup of Nations editions.
The 2004 African champions have only won the third-place match once in their history, back in 1962.