Wenger was banned for two European matches on Monday for failing to abide by the conditions of a previous suspension in last week's play-off round first leg which Arsenal won 1-0.
Arsenal appealed and then requested that the ban start after the case had been heard by European football's governing body.
"The UEFA appeals body has granted a stay of execution to the appeal," said UEFA on its website.
"The appeals body will take a decision in due time but not before Arsenal's Champions League game against Udinese in Italy.
"Without today's decision by the appeals body the manager's suspension would have taken effect for the play-off second leg at Udinese."
Wenger's original ban stemmed from his behaviour in last season's round of 16 tie at Barcelona.
The Frenchman was then seen sitting in the stands and talking on a mobile phone in last week's first leg, passing instructions to the team bench.
UEFA rules stipulate that coaches cannot communicate with their teams while they are serving a touchline ban.
Arsenal have taken part in the Champions League group stage for the past 13 seasons but that run could end on Wednesday.
The London club have been hit by injuries this season and the sale of captain Cesc Fabregas to Barcelona.
They have taken one point from two Premier League matches although that would pale into insignificance if they missed out on qualification for the Champions League group stage.
