Wenger, who is 65 on 22 October, signed a new three-year deal in May.
"The biggest challenge we're going to face as a club is that transition from Arsene to the next manager," said Gazidis.
"We have a giant who's managing us. Arsene has put the club in a great, great position."
Arsenal have qualified for the Champions League for 17 consecutive seasons under Wenger and the Frenchman led the Gunners to their first piece of silverware in nine years in May when they beat Hull in the FA Cup final.
Appointed in September 1996 as a relative unknown whose previous post had been in charge of Japanese side Grampus Eight, Wenger is currently the longest-serving manager in English league football.
He steered Arsenal to the Premier League title in 1997-98, 2001-02 and 2003-04.
The club moved from Highbury to the newly-built Emirates Stadium at the start of the 2006-07 season and Gazidis believes the extra revenues generated have helped Wenger in the transfer market, with Mesut Ozil and Alexis Sanchez brought in for a combined total of approximately £77m over the past year.
"The last five years of unlocking our international and our commercial revenues is so important for the club," Gazidis added.
"It allows us to go out and, if the manager believes in someone like Mesut Ozil, he can buy him. It's the same with Alexis Sanchez."
Gazidis added: "Unlike the situation two or three years ago when we were really financially challenged and losing our top players, we are signing our top players to long-term contracts - guys like Jack Wilshere and Aaron Ramsey."
Former Arsenal defender Martin Keown agreed with Gazidis, but believes Wenger could have a role to play at the club even after leaving as manager.
"I could see him floating around the training ground in a non-confrontational way, just keeping an eye on things," said Keown.
"Who wouldn't want a man of that experience and quality working alongside them?"
Arsenal's biggest challenge will be finding manager Arsene Wenger's replacement when he leaves, according to chief executive Ivan Gazidis.