The Ghanaian received a straight sending off in the goalless draw at The John Smith's Stadium following a challenge on Jonathan Hogg, leaving the Swans to sweat it out for 79 minutes with 10 men.
After the match, Swansea boss Carlos Carvalhal stated that they were considering appealing the decision, as his striker did not deserve the marching orders.
“Swansea City have reluctantly decided against appealing the red card shown to Jordan Ayew at Huddersfield Town on Saturday,” the club have announced.
“Swans forward Ayew was sent off after a challenge with Terriers midfielder Jonathan Hogg.
“Boss Carlos Carvalhal felt the decision was harsh, arguing after the game that both players had made similar challenges as they competed for the ball.
“But the Swans have opted not to appeal referee Michael Oliver’s decision, meaning Ayew will be banned for the club’s next three matches.
“The Swans were conscious that if an appeal is deemed frivolous by the Football Association, suspensions can be extended.
Jordan's red card is the fastest received by any player in the English topflight this season.
Adjudged the club's best player in both January and February, his absence will be a big blow to Swansea, who are currently caught up in fierce a relegation fight.