The Democrat from Virginia said he thinks other methods should be used to fix the issues in the sector. On Tuesday, he rolled out the first in a series of bills aimed at regulating Facebook and other social media companies.
"These companies have enormous, enormous power and we do need to introduce more competition," said Warner, vice chairman of the Senate Select Committee on Intelligence. He began studying Facebook as part of the committee's investigation into Russia's involvement in the 2016 presidential election.
However, when it comes to addressing antitrust issues, he has concerns about trying to dismantle the largest companies.
"These are now companies that don't exist in an American-only vacuum. These are all global companies," the senator said on "Power Lunch."
"I have some concern, as somebody who is very concerned about the rise of China, that if we were to kind of chop off the legs of Facebook and Google, that they might be replaced by Alibaba, Baidu, Tencent — companies that are totally enmeshed with the Chinese government in their global economic plan," he added.
Alibaba is China's largest e-commerce platform and Tencent is the country's internet giant, while the search engine Baidu is known as China's answer to Google.
Alibaba, Baidu and Tencent did not immediately respond to requests for comment.
Warner said there are ways to introduce more competition and transparency to the U.S. tech sector — which he thinks should be done before there is talk of breaking up the big companies. He also wants to tackle the manipulative behavior, address privacy issues and content around hate speech
His first bill, introduced with co-sponsor Sen. Deb Fischer, R-Neb. on Tuesday, bans online platforms with more than 100 million monthly active users from using so-called dark patterns. The term refers to interfaces designed to coax users into taking actions that often result in giving up more information than the user realizes — such as prompts to access phone and email contacts in order to keep using the platform.
Warner's next piece of legislation is expected to address data transparency, requiring tech companies to disclose the value of user data and how companies profit from it, as Axios first reported.
"This is going to be an issue that is not going to go away. It's going to only potentially get worse. And we've got to roll up our sleeves … and solve it," said Warner.
— CNBC's Kayla Tausche and Mary Catherine Wellons contributed to this report.