The FIA issued a statement earlier this week indicating that its compliance department was "looking into the matter" of an allegation that confidential information had been passed from an FOM employee to a team principal, while not naming the Wolffs.
However, it was a clear reference to the couple in the wake of a magazine article that contained the allegation and suggested that rival team bosses had complained.
Subsequently, all the other F1 teams issued statements confirming that they hadn't made any such complaint.
The FIA then issued a second statement on Thursday explaining that there was no ongoing investigation.
F1 Academy boss Susie Wolff questioned the governing body's response, noting that "what happened this week is simply not good enough".
Toto Wolff also said Mercedes is "in active legal exchange with the FIA".
Speaking at a press conference at the governing body's prize-giving gala in Baku, Hamilton jumped to the defence of the Wolffs and criticised the FIA's actions.
"It's been a challenging week," Hamilton said.
"I think a disappointing week really to see that the governing body of our sport has sought to question the integrity of one of the most incredible female leaders we've ever had in our sport, with Susie Wolff, without questioning, without any evidence, and then just saying 'sorry' at the end.
"And that's just unacceptable. We've got a lot of great people within the sport that are doing amazing work. There is a constant fight to really improve diversity and inclusion within the industry.
"But it seems that there are certain individuals in the leadership within the FIA that every time we try and make a step forward, they're trying to pull us back. And that has to change."
Hamilton also stressed that motorsport as a whole has to address issues of diversity.
"I think this is a global sport," he said. "And we have such an incredible opportunity and a natural responsibility to be leaders of change.
"And as we're travelling to all those countries around the world, we have a responsibility to make sure that we're pushing in the right direction.
"So I do want to acknowledge that there are a lot of people that are doing great work. But we need to make some changes to make sure that we're all pushing in the right direction."
Hamilton also praised Toto Wolff, who has been his team boss for the decade of his tenure at Mercedes, as the team looks to return to fighting at the front in F1 next year.
"Toto is an amazing leader," he said. "I've known him for a long time. We joined the team at the same time.
"It's been an interesting journey for both of us to both grow with the team, to see his vision grow and progress within the structure of the team. He hasn't lost an ounce of his competitiveness he's massively competitive.
"You see it on TV even when he's sitting at his little desk in the garage. Trying to find a balance in life of work life and family life I think he's done a really great job there.
"But I think just continuing to push everyone - yesterday again we were talking to the team together. He's a very, very approachable leader, and I think people can relate to him, to his emotions and just to his compassion, or his drive.
"He's very understanding. I think it's definitely not been easy for anybody in the team when you're working towards something, but it's not quite going the way you want it.
"I think there's been many lessons, and I've been really proud to see the progress that he's made just as an individual and as a human being as well."