Johnson bit Joe Allen's shirt with his teeth in the aftermath of a melee following a sending off for Stoke's Oghenekaro Etebo.
The incident was not caught by the match official, but was seen on camera , prompting the FA to step in.
Johnson will miss a total of five games, with the additional match coming due to yellow card accumulation.
"Bradley Johnson has been suspended for four games after he was found to have committed an act of violent conduct for which the standard punishment would be clearly insufficient," the FA said in a statement.
"The Derby County player was involved in an incident with Stoke City's Joe Allen during Wednesday's game [28 November 2018] which was not seen by the match officials but caught on camera.
"Johnson denied the charge of violent conduct with an Independent Regulatory Commission then considering The FA's allegation that the three-match sanction should be increased.
"In addition to the suspension for violent conduct, the player will also serve a one-match ban for accumulating five cautions."
The 31-year-old midfielder has been with the Championship club since 2015 after previously featuring for the likes of Norwich, Leeds, and Northampton Town.
"Derby County does not expect, nor condone, any of its players to behave in the manner witnessed in the incident on Wednesday evening," the club said in a statement.
"The club will be conducting its own internal disciplinary hearing in relation to the matter and as such will make no further comment."
Stoke midfielder Joe Allen played down the incident, the Wales international saying he was not bitten.
“People asked me at half-time what had happened and suggested I’d been bitten but to clear it all up, that didn’t happen," he said after the match.
“He might have caught a bit of my shirt but I think we can lay that one to rest.”