Wolff, director of Formula 1's academy series for aspiring female drivers, revealed Wednesday she lodged a criminal complaint in the French courts over a controversial inquiry into her conduct last year.
Wolff and her husband, Mercedes Formula 1 team principal Toto Wolff, were the subject of an investigation into an alleged conflict of interest.
The probe arose in December after a magazine report claimed that other team principals were concerned Toto Wolff was benefiting from information shared by his wife.
But the FIA ended its investigation just two days after announcing its compliance department was looking into the matter.
Both Formula 1 and Mercedes strongly rejected the accusations and made clear their frustration with the FIA's handling of the matter.
"I'm incredibly proud of Susie, she is so brave and stands for such great values, she is such a leader," said Mercedes' seven-time world champion Hamilton ahead of the Australian Grand Prix.
"In a world where often people are silent, for her to be standing up sends such a great message and I love that she is taking it out of this (F1) world, because there is a real lack of accountability within the sport and the FIA.
"Things happen behind closed doors, there is no transparency, there really is no accountability."
In a social media post at the time the allegations arose, Susie Wolff branded them as "intimidatory and misogynistic".
"There has still not been any transparency or accountability in relation to the conduct of the FIA and its personnel in this matter," she said on social media Wednesday.
"I feel more than ever it is important to stand up, call out improper behaviour and make sure people are held to account. Whilst some may think silence absolves them from responsibility - it does not."
Hamilton said he hoped her stance would bring about change.
"It is still a male-dominated sport. We are living in a time where the message is if you file a complaint, you will be fired," he said.
"And that is a terrible narrative to be projected to the world, especially when we talk about inclusivity."
