Both players were dismissed for their part in the incident at Carrow Road on Tuesday - with Newcastle also appealing the Frenchman's suspension, although that has been dismissed by the Football Association.
Both players had been hit with three-match bans after Remy headbutted the former Leeds United midfielder, who reacted furiously.
Remy's bad fortune in the game was compounded by the dismissal, as he had previously hit the woodwork three times in the 0-0 draw.
An FA statement read: "The claim involving Norwich’s Bradley Johnson was upheld meaning his three-match suspension is withdrawn.
"The claim involving Newcastle’s Loic Remy was dismissed therefore his three-match suspension remains with immediate effect.
"Both players had been dismissed for violent conduct."
Though Johnson is free to play for Norwich immediately, Remy's absence could be keenly felt when Newcastle contest the Tyne-Wear derby with Sunderland on Saturday.
Luuk de Jong arrived at St James' Park on loan from Borussia Monchengladbach on Wednesday, but may be short of fitness, having not made an appearance for the Bundesliga side since December 22.
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