He is the son of former U.S. Representative Ron Paul of Texas.
Rene Boucher, 59, of Bowling Green, was arrested shortly after the incident Friday afternoon, state police said.
Paul spokeswoman Kelsey Cooper released a statement Saturday about the incident after being contacted for comment.
The Bowling Green Daily News, citing an arrest warrant, said Paul told police his neighbor came on to his property in a gated community just east of Bowling Green and tackled him from behind.
"Senator Paul was blindsided and the victim of an assault", it stated. Stay with 8News online and on air for the latest updates.
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However, Boucher is an anesthesiologist and pain specialist in Bowling Green, who developed a product called Therm-a-Vest.
It is not known if Senator Paul knew his attacker. "Thank you for your thoughts and prayers", Paul said on Twitter on Sunday morning, referring to his wife. At the time the report was made Paul was being seen by a physician and the extent of any rib injury was unclear, the complaint says. But more, recently Paul has emerged as a leading defender of Trump's policies and has golfed with the president at Trump's Virginia golf course.
Records show Boucher's home is also in Bowling Green.
The investigation by Weaver is continuing, and no other details were immediately available.
CNN was unable to reach a representative of Boucher on Saturday night.