The Poland international had his appeal claim of wrongful dismissal rejected following an independent regulatory commission hearing on Tuesday.
Fabianski was sent off in Swansea's 3-1 Premier League defeat to West Ham at the Liberty Stadium on Sunday.
The keeper was shown the red card by referee Chris Foy in the 68th minute for a professional foul on Diafra Sakho.
Swansea manager Garry Monk claimed Sakho handled the ball before being fouled by Fabianski, leading to the club's appeal.
The FA's independent regulatory commission has rejected Swansea's appeal however, ruling Fabianski out of Sunday's clash with Spurs at the Liberty Stadium.
"Swansea City's Lukasz Fabianski will serve a one-match suspension with immediate effect after his claim of wrongful dismissal was dismissed following an Independent Regulatory Commission hearing today," the FA confirmed in a statement.
"Fabianski was dismissed for denying a goal scoring opportunity against West Ham United on 7 December 2014."
Source : PA
Source: PA