The Australian custodian picked up the knock in the World Cup play-off with Uruguay in Montevideo, which The Socceroos lost 3-0.
"It is disappointing that he has picked up this injury," said Boro boss Steve McClaren.
"We are going to have it checked out by a specialist before we know what actions, if any, we have to take and how long he may be out."
Experienced netminder Mark Crossley is likely to deputise for Schwarzer after keeping three clean sheets in the number one's absence.
