Wright limped off after 20 minutes against Newcastle and was replaced by Nigel Martyn, who will now step into the first team spot in his place.
"Clearly there is some problem, so we will have a good look inside the knee, though we don't think there is anything significantly wrong," Everton's head physio Mick Rathbone told the club's official website.
"All the scans have been normal and Richard has been able to train but sometimes if he catches the ball wrong when kicking then he feels some pain."