The 25-year-old had been managing the issue for several weeks before being forced off after 30 minutes of France’s semi-final defeat to Spain.
Following his return to London and assessment by a specialist, Arsenal confirmed that surgery will not be required.
Instead, Saliba will undergo a managed recovery programme. The defender also missed France’s bronze-medal defeat to England.
The Frenchman made 50 appearances for Arsenal last season, helping the Gunners win their first Premier League title in 22 years and reach the Champions League final.
His absence will be a major concern for Mikel Arteta, with Arsenal facing Manchester City in the Community Shield on 16 August before beginning their title defence against promoted Coventry City five days later.