The 28-year-old also missed several weeks last season after injuring his hamstring while playing for Melbourne Victory.
Nabbout's absence will leave a major hole in City's line-up, and it remains unclear how many games he'll miss given that the A-League fixture is still yet to be finalised for numerous matches.
City will be back in action on Sunday when they take on Adelaide United at Coopers Stadium.
Uruguayan midfielder Adrian Luna will also miss the match against Adelaide after being sent off against Brisbane.
Nabbout initially signed for Perth Glory after leaving Victory last season, but that deal fell through due to the difficulty of getting him into Western Australia while the borders were shut.
After his Glory contract was terminated by mutual consent, he signed a one-year deal with Melbourne City.