Wenger is under mounting pressure after overseeing the club's worst start to a season in 58 years.
With five Barclays Premier League games gone, Arsenal have just one win to their name - against newly-promoted Swansea - and sit 17th in the table.
Wenger endured the humiliation of a 8-2 defeat at rivals Manchester United and his misery deepened on Saturday when he saw his team put in an abject defensive display to lose 4-3 to strugglers Blackburn.
Gazidis was adamant this morning that the board was fully behind the manager.
Wenger has looked increasingly strained of late due to his team's poor performances, but Gazidis insists Arsenal's 61-year-old boss is not about to walk out on his post, nor is he about to be sacked.
"He is not going to walk out," Gazidis said. "There is absolutely no issue about Arsene leaving the club or the club pushing him out.
"He did not suddenly become a bad manager or somebody who became out of touch with the game. It is complete nonsense."
Wenger's 15 years in English football means he is likely to be considered as a potential replacement for England manager Fabio Capello.
The Italian's contract expires next summer, but Gazidis made his position clear when he was asked whether the club had considered the prospect of Wenger being on the Football Association's shortlist next year.
"He is under contract to Arsenal and he always honours his contract. It's not an issue," he said.
Much of the fans' anger stems from Wenger's refusal, unlike many of his rivals, to sanction big-money signings.
That anger was greater than ever this summer as the Frenchman could only sign the likes of Yossi Benayoun and Mikel Arteta after seeing Samir Nasri and Cesc Fabregas depart for Manchester City and Barcelona respectively.
The sale of both players so close to deadline day left the club little time to bring in more established replacements, but Gazidis denies Wenger resorted to panic buying.
"Some people have the perception that there was some panic buying in the window but that's not what happened," Gazidis said.
"I'm not sure we could have handled things differently. We made some signings early and some late.
"We obviously had an uncertainty about Fabregas and Nasri. Ideally we would have liked them resolved earlier for proper value but we are the ones who know what really happened in all of that.
"You will have to let this run for a season or two before we can really look back and fully assess (this year's transfers)."
Gazidis moved to ease supporters' concerns by promising that Wenger will have major funds available to him when the transfer window opens in January.
"We have kept some powder dry and we have done that deliberately because of how the market was this summer," Gazidis added.
"I don't want to build up expectations but certainly in January and next summer there are funds available to invest in a significant way to bolster the team.
"But the important thing from our perspective is discipline. We are not going to spend money just because we are under short-term pressure."
Gazidis also launched a staunch defence of Arsenal owner Stan Kroenke.
The American has not watched a Gunners game this season and rarely speaks in public - leading to him being dubbed "Silent Stan", but Gazidis thinks the tag is unfair.
"The truth is that Stan is not silent," Gazidis added. "He has been very involved throughout and for a number of years with the club.
"Stan has said that he will talk to the fans the next time he is in the UK and he will."
Gazidis also expects the sports tycoon to take in a game at the Emirates Stadium next month.
"We are arranging a meeting to talk about this now," Gazidis said. "It will be some time in October and he will do some press around that time as well.
"He is not somebody who pushes himself into the limelight but he is not the 'Silent Stan' you might imagine. He is a big sports fan."