Gibbs was mistakenly sent off by referee Andre Marriner against Chelsea on Saturday in a case of mistaken identity after Oxlade-Chamberlain had handled the ball on the line.
The defender has now seen his red card rescinded while Oxlade-Chamberlain has also escaped punishment due to it being judged that the ball was going wide of goal.
"An Independent Regulatory Commission today heard two claims from Arsenal, one of mistaken identity and the other of wrongful dismissal, both in relation to Saturday's game against Chelsea at Stamford Bridge," read an official FA statement.
"The Commission ruled that the dismissal of Kieran Gibbs was a case of mistaken identity and transferred this to his teammate Alex Oxlade-Chamberlain.
"Subsequent to deciding this matter, the Commission then considered Arsenal's claim for wrongful dismissal in relation to Oxlade-Chamberlain.
"This claim was upheld meaning Oxlade-Chamberlain will not serve any suspension with the standard punishment withdrawn with immediate effect."
It was confirmed on Monday that Andre Marriner would not face action for his part in the incident.