WASHINGTON—A House oversight committee on Friday said it was launching an investigation into whether the White House improperly influenced the Federal Communications Commission on its new rules for how broadband providers treat traffic on their networks.

Rep. Jason Chaffetz (R., Utah), chairman of the House Oversight and Government Reform Committee, wrote to FCC Chairman Tom Wheeler on Friday demanding all documents and communications between the FCC and the White House or other executive-branch agencies on the issue, along...