Kennedy, a member of the Senate Judiciary Committee, will get a chance to question Zuckerberg when the CEO appears before a joint hearing of the Senate Judiciary and Commerce committees on Tuesday. Zuckerberg is also expected to give testimony before the House Energy and Commerce Committee on Wednesday.

"I'm hoping that Mr. Zuckerberg won't just, I don't know, pull things out of his orifices. That he'll talk frankly about what Facebook can and cannot do," the Republican from Louisiana said on " Power Lunch ."

Facebook CEO Mark Zuckerberg needs to be candid and forthcoming when he testifies in front of Congress this week, Sen. John Kennedy told CNBC on Monday.

Facebook CEO Mark Zuckerberg is seen through reflective glass as he sits in the office of Senator Bill Nelson (D-FL) while he waits for a meeting in the Hart Senate Office Building in Washington, U.S., April 9, 2018.

Facebook is under scrutiny after reports that research firm Cambridge Analytica improperly gained access to the personal information of as many as 87 million Facebook users. The company also has faced questions after reports of Russian meddling during the 2016 presidential election.

Kennedy said the most "frightening" issue is whether Facebook really has control or whether the company has lost control over what's happening on its social media platform.

He also wants to know who owns the data — Facebook or the users, as well as if there is an ability for users to erase his or her data.

"It's swell I can go on Facebook and see what my high school buddies had for dinner last night but do you think it's fair in exchange for that that I agree to give up all of my personal data to just about anybody in the Milky Way?" he said.

Kennedy also has issues regarding antitrust and whether it's in the public's interest that Facebook is growing larger.

Earlier Monday, the House Energy and Commerce Committee released the prepared testimony Zuckerberg is expected to deliver.

In it he said, "It's clear now that we didn't do enough to prevent these tools from being used for harm as well. That goes for fake news, foreign interference in elections, and hate speech, as well as developers and data privacy. We didn't take a broad enough view of our responsibility, and that was a big mistake. It was my mistake, and I'm sorry. I started Facebook, I run it, and I'm responsible for what happens here."

Kennedy said he isn't out to hurt the social media giant.

"I come in peace," he said. "I don't want to regulate them half to death but I think it's pretty clear the digital Promised Land is not all milk and honey. We've discovered some impurities in the punch bowl."

That said, when asked what Congress could do to regulate social media, Kennedy replied, "We can do anything we want to."

Zuckerberg was on Capitol Hill on Monday meeting with lawmakers ahead of his testimony.

Sen. Bill Nelson, who met with the CEO, told reporters afterward that he told Zuckerberg that he thinks social media needs to be regulated.

"If we don't rein in the misuse of social media none of us are going to have any privacy anymore," said Nelson, a Florida Democrat.

— CNBC's Sara Salinas contributed to this report.