The former Arsenal man picked up the injury at Charlton, which stops him from kicking properly - and he suffered a recurrence of the problem against Newcastle United on Saturday.
"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."
Nigel Martyn will continue in goal whilst Wright is sidelined with Steve Simonsen coming in on the bench.
Everton are also waiting on the fitness of Wayne Rooney before Sunday's clash with Middlesbrough, after he picked up an ankle problem.
"Wayne is okay, we don't think it is too serious and hopefully he will train in the middle of the week," Moyes added.
"It is a case of waiting and finding out."
