The 34-year-old was sent off by referee Mike Jones just four minutes into Saturday's 2-0 Barclays Premier League defeat by the Tigers at the Stadium of Light after felling striker Shane Long as he headed towards goal.
FA disciplinary chiefs have confirmed he will receive a one-match ban for denying a goalscoring opportunity, and another as it was his second red card of the season.
The former Manchester United defender will miss Wednesday night's league trip to Manchester United and the FA Cup fifth-round tie against Southampton on Saturday as a result.
However, he will be available for Sunderland's league visit to Arsenal on February 22 and more importantly, the Capital Cup final clash with City at Wembley the following weekend.
Brown has actually been sent off three times this season, although his first red card was rescinded on appeal.
He received his marching orders from referee Kevin Friend during the 2-0 defeat at Stoke on November 23 for a challenge on midfielder Charlie Adam, but later had a claim for wrongful dismissal upheld.
However, he was suspended for three games after being dismissed for a crude tackle from behind on Norwich striker Ricky van Wolfswinkel during a 0-0 draw at the Stadium of Light on December 21.