The centre-back was dismissed just four minutes into Saturday's 2-0 loss to Hull City and will now miss one game for the red card and one for a previous offence against Norwich
The 34-year-old centre-back received his marching orders from referee Mike Jones just four minutes in at the Stadium of Light after bringing down Hull striker Shane Long, who was bearing down on goal.
Sunderland went on to lose the game 2-0, with Long and Nikica Jelavic both registering.
The dismissal marked the third time this season Brown has seen red in a Premier League fixture, after previous reds against Stoke City and Norwich City.
His red card against Stoke was subsequently overturned by the FA on appeal.
Brown receives a standard one-match ban for denying a clear goalscoring opportunity, as well as an additional game due to his upheld sending off against Norwich.
The suspension comes as a blow to manager Gus Poyet, who will be without the experienced defender for the Premier League visit to Manchester City on Wednesday and Saturday's FA Cup encounter with Southampton.