In a statement, the Black Eagles said that Montero, 22, underwent a Magnetic Resonance Imaging (MRI) scan earlier Friday as he suffered a Grade 2 knee sprain.
Montero was injured during Besiktas' Ziraat Turkish Cup match against Ittifak Holding Konyaspor on Thursday and had to go off the pitch. His treatment has begun.
Besiktas advanced to the Turkish Cup semifinals, beating Konyaspor on penalties.
The Istanbul club did not give any details about his return.
Montero, who was loaned from Atletico Madrid in September, had 14 appearances this season for Besiktas.
