The 26-year-old, who was substituted in the second half at White Hart Lane after colliding with Jermain Defoe, was taken to hospital where X-rays confirmed the fracture of his left forearm.
"Craig's in a lot of pain," manager Steve Bruce told the club website (www.safc.com).
The club, who have Hungarian international Marton Fulop and youngster Trevor Carson as reserve goalkeepers and are eighth in the league, said they did not know how long Gordon would be out of action.
Gordon, who moved to Sunderland from Hearts in 2007, had been due to join the Scotland squad in the next few days for a friendly against Wales.
(Reporting by Alan Baldwin; Editing by Sonia Oxley)