They have been fined after being found guilty of failing to control their players during the bad-tempered goalless draw at St James' Park on August 13.
Gunners forward Gervinho was sent off in the second half for striking Magpies midfielder Joey Barton after the pair had squared up following what the home side claimed was a dive.
Arsenal midfielder Alex Song will also serve a three-match ban for stamping on Barton's leg in an incident not seen by referee Peter Walton.
An FA statement: "An independent regulatory commission today found both Newcastle United and Arsenal guilty of failing to control their players.
"The charges relate to an incident during their recent league fixture at St James' Park on Saturday 13 August 2011.
"Both clubs denied the charge and requested a non-personal hearing. In each case, the charge was proven by the regulatory commission and both clubs have been fined £30,000."