The Bournemouth skipper was sent off in the 3-3 draw with Arsenal for a challenge on Aaron Ramsey with the Cherries winning 3-2 at the time.
The Cherries appealed Francis' red card, but the FA have since turned down the appeal.
An FA statement read: "Simon Francis will serve a three-match suspension with immediate effect after his claim of wrongful dismissal was rejected today, following an Independent Regulatory Commission hearing.
"The Bournemouth defender was sent off for serious foul play during the game against Arsenal on Tuesday 3 January 2017".
After the game, Bournemouth manager Eddie Howe said that he thinks his side were "harshly treated".
"I didn't think it was a sending off on first view," he said.
"I don't think his feet were raised enough on contact to warrant a red card. That was my view the first time and my view when I watched it again. So I think we were harshly treated there".