The injury occurred during Nigeria's 1-1 draw against South Africa on Tuesday, and the club has confirmed that Aina will be absent for an uncertain period of time.
The club has expressed its concern for Aina's well-being and wishes him a speedy recovery.
Aina, a 28-year-old former Chelsea player, made 35 league appearances for Forest last season.
The team is set to face Arsenal on Saturday, and fans can follow the match through various streaming platforms.