Clinton dodged the object, which may have been a shoe, and joked about it during her remarks at the Mandalay Bay hotel and casino, the newspaper said.
"Is that somebody throwing something at me?" Clinton asked, according to the Review-Journal. "Is that part of Cirque du Soleil?"
A hotel spokeswoman told Reuters she had no information on the incident. A spokesman for Clinton did not immediately reply to a request for comment.
Las Vegas police, who reportedly arrested the protester, referred calls to the Secret Service in Washington, D.C., which could not immediately comment.
Clinton had been speaking to more than 1,000 people attending a metal recycling conference in Las Vegas.