In a statement on their website, Sunderland announced Gordon fractured a bone in his arm and underwent an operation to repair the damage yesterday.
Sunderland have not said how long he will be out for but he will miss the start of the new campaign.
"He is set to miss the start of the season as he undergoes rehab on the damaged arm," said the statement.
Gordon, who joined the Black Cats for £9million from Hearts - a British-record fee for a goalkeeper - in 2007, made 31 appearances last season in another campaign disrupted by injury.
The 27-year-old suffered a broken arm in November last year after being caught by what he described as a "poor challenge" from Tottenham's Jermain Defoe.
He returned in January and enjoyed his best run of form on Wearside, a series of impressive displays helping the club to a 13th-placed finish in the Premier League.
His latest injury blow is likely to see him miss Scotland's opening two European Championship qualifiers against Lithuania and Liechtenstein while he must also be doubtful for October's clashes with the Czech Republic and Spain.