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.
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.
Bizarre Jose Mourinho statement aims to pre-empt punishment after Fenerbahce boss clashes with Galatasaray counterpart
'Andy Robertson has a decision to make as a player, where you either roll your sleeves up and give someone great competition or you accept decisions and say that your time is done.' Alan Shearer on the conundrum facing Arne Slot's Liverpool
