Hamilton hopes Wolff's legal action will bring greater transparency and accountability to the FIA.
"Firstly, I'm incredibly proud of Susie," Hamilton said. "I think she's so brave and she stands for such great values.
"She's such a leader, and in a world where often people are silenced, for her to be standing up sends such a great message. And I love that she's taken it out of this world - fighting it from outside because there is a real lack of accountability here within this sport, within the FIA, things that are happening behind closed doors.
"There is no transparency, there is clearly no accountability, and we need that. I think the fans needs that. How can you trust the sport and what is happening here if you don't have that?
"So hopefully this stand that she's taken now will create change, will have a positive impact, and especially for women."