The Scotland international was charged by the FA on Monday after appearing to stamp on the leg of Arsenal's Olivier Giroud during Saturday's Premier League match at the Britannia Stadium.
Although the incident was not spotted by match officials, it was caught on video.
Stoke reacted with surprise and announced they would "vigorously appeal" against the decision, pointing to a lack of intent on their player's part.
However, an Independent Regulatory Commission has decided to uphold the charge, meaning Adam will now miss games against Norwich City, West Ham and Aston Villa.
An FA statement on Wednesday read: "Stoke City's Charlie Adam will serve a three-match suspension with immediate effect after an FA charge for violent conduct was found proven.
"The incident with Arsenal's Olivier Giroud, which was not seen by the match officials but caught on video, occurred during the fixture between the two sides at the Britannia Stadium on Saturday 1 March 2014.
"Adam had denied the charge, but it was found proven at an Independent Regulatory Commission hearing today (Wednesday 5 March 2014)."
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