In recent weeks, sporting director Steve Nielsen and single-seater technical director Tim Goss have both left the FIA. Their departure comes after the exit of Deborah Mayer as head of the FIA Women in Motorsport Commission.
Speaking to The Daily Telegraph, Wolff said it is "concerning" that several key people have "suddenly" quit, with Nielsen only being in the job for a year amid suggestions that he had grown frustrated with the direction of the FIA's F1 operation.
"It's concerning to see so many good people leaving," Wolff said. "Losing Steve Nielsen is a big blow. I couldn't think of a more knowledgeable and fair sporting director.
"As a leader, it's about the culture and environment you create for people to thrive. When people as competent as these leave an organisation there is a vacuum. That's clear. And you've got to ask yourself why is it suddenly that so many people have decided to call it a day?
"What [the FIA] needs is stability. The FIA is one of three key stakeholders of the sport [along with FOM and the teams].
"And as the leadership of these organisations, we need to set the tone for everybody else. We need not only to say that we're acting transparently, and ethically, but actually to live to that standard every single day."
The recent departures come amid a turbulent end of the year for the FIA after it was embroiled in controversy around its short-lived probe into an alleged conflict of interest between Toto and Susie Wolff.
The probe was soon shut down after facing a united front from F1 and its 10 teams defending the Wolffs.
While Wolff didn't comment on any further legal steps, he said the way the FIA's probe was conducted was "very, very damaging".
"I think because we have a billion people or more that watch our sport, we are role models," he added.
"And we need to be wary of the impact of what we do and what we say. What has been said and the way it was done was very, very damaging."
