Cambridge Analytica, which worked on Facebook ads for the Trump campaign, is accused of improperly gaining access to 50 million profiles before the 2016 election. Cambridge Analytica has called the allegations "false" and on Tuesday the board suspended CEO Alexander Nix.
Zuckerberg, who broke his silence on the scandal in a Facebook post Wednesday, has expressed a willingness to testify.
"What we try to do is send the person at Facebook who will have the most knowledge," Zuckerberg said in an interview with CNN on Wednesday. "If that's me, then I am happy to go."
In his initial statement, the CEO said the company will take measures to ensure user privacy, including investigating all apps with access to Facebook data. "We have a responsibility to protect your data, and if we can't then we don't deserve to serve you," Zuckerberg wrote in the post.
Walden said his committee has already spoken to Facebook representatives, but he said there are still unanswered questions.
"Is this one incident the only one? Did it happen in prior campaigns? We've got to get to the bottom of it," he said, noting that as the founder, Zuckerberg knows "everything about the company."
However, Walden isn't necessarily championing tough regulation of Facebook and the industry.
"I'm into light-touch regulation, not heavy-handed government," he said. "We want to look into it and say 'are America's laws keeping pace? Can it self-regulate? Is more needed?' I don't think we have the answer to that question yet, that's why we need to start at the top."
Facebook COO Sheryl Sandberg told "Closing Bell" on Thursday that the company was open to regulation.
"Mark [Zuckerberg] has said, 'It's not a question of if regulation, it's a question of what type,'" Sandberg said.
— CNBC's Sara Salinas and Jillian D'Onfro contributed to this report.