The goalkeeper was given his marching orders by Michael Oliver having tripped Bafetimbi Gomis as he ran through on goal, and the Blues were hopeful the decision would be overturned.
But the FA felt there was not sufficient evidence to support their claim and the Belgium international will now miss Sunday's clash with Manchester City at the Etihad Stadium.
A statement from the FA read: "A claim of wrongful dismissal submitted by Chelsea in relation to Thibaut Courtois has been unsuccessful following an Independent Regulatory Commission hearing earlier today.
"The goalkeeper was dismissed for denying an obvious goal scoring opportunity in the 52nd minute of Chelsea's game against Swansea City at Stamford Bridge on Saturday (8 August 2015).
"Therefore, the player's one-match suspension, which is the standard penalty for this offence, remains with immediate effect.
"For a club to be successful with a claim of wrongful dismissal, it must prove to an Independent Regulatory Commission via written and/or video evidence that the match referee made an obvious error."
Asmir Begovic, who signed for the club this summer from Stoke City, will be in line to make his first start for the Blues in Sunday's visit to the Etihad Stadium.
