The left-back was sent off in the first half of the Gunners' 6-0 defeat to Chelsea at Stamford Bridge, despite Alex Oxlade-Chamberlain committing the handball offence
Gibbs was shown the red card in a case of mistaken identity during the 6-0 defeat to Chelsea, after Oxlade-Chamberlain handled an Eden Hazard effort in the penalty area with his side already trailing.
Hazard converted the resulting penalty, while Gibbs was left confused as to why he had been dismissed, with Oxlade-Chamberlain appearing to tell Marriner he was the guilty party himself.
"Incidents of mistaken identity are very rare and are often the result of a number of different technical factors," a statement from refereeing body Professional Game Match Officials Limited read.
"Whilst this was a difficult decision Andre is disappointed that he failed to identify the correct player.
"He expressed his disappointment to Arsenal when he was made aware of the issue."
The defeat, which occurred on Arsene Wenger's 1,000th game in charge of the club, saw the Gunners slip seven points behind Chelsea in the Premier League, though they do have a game in hand on the Stamford Bridge outfit.