The 28-year-old Belgium international was reportedly close to joining West Ham on September's transfer deadline day, but the proposed deal collapsed.
With Leicester adjusting to the financial challenges of League One following successive relegations, the player’s departure removes one of the club's highest earners from their wage bill.
The defender made more than 130 appearances for Leicester, although he featured just once this season, against Barnsley earlier this month.
Faes spent the second half of last season on loan at Monaco, who declined to make his move permanent.
His departure continues Leicester's extensive squad overhaul, which has already seen Jannik Vestergaard, Abdul Fatawu, Hamza Choudhury and Harry Winks leave the club.
Neither Leicester nor Shabab Al Ahli has disclosed the transfer fee or further financial details of the agreement between the clubs.