There was an agreement between the players and their goalkeeper to break their fast in this way.
On both occasions his 'injury' prompted his teammates to rush to the sidelines to eat dates and drink water before taking to the field again.
During their first match against Portugal, Nice keeper Hassen went down in the 58th-minute with an 'injury'.
Just six minutes later, Tunisia - who are in England's group at the World Cup - scored and the game finished 2-2.
On Saturday against Turkey, Hassen lay flat on his back after a corner in the 49th-minute, allowing his team-mates to leave the pitch for food and water. He stayed down for around a minute.
Tunisian sports reporters were the first to point out that Hassen's injuries both coincided with sunset, which is when Iftar - or the breaking of the fast - begins.
Freelance reporter Souhail Khmira tweeted that there is 'an agreement' between the players and their goalkeeper to break their fast in this way.
It does not appear that Turkey, another mostly Muslim nation, had any such arrangement in place when they played Tunisia.
Hassen has since been teased on Twitter, including by fellow footballer Chaker Alhadhur, who joked: 'It's all right now, we know you were pretending.'