State troopers responded to a call to the senator's residence at 3:21 p.m. Friday.
Boucher was booked into the Warren County Regional Jail.
Kentucky State Police says the Federal Bureau of Investigation is now investigating to see if the assault was politically motivated.
Paul's office said in a statement the former Republican presidential candidate "was blindsided and the victim of an assault". Rand Paul says he has received overwhelming support following an injury after an assault at his home. "Thank you for your thoughts and prayers", Paul said on Twitter on Sunday morning, referring to his wife. Hodges did say that Boucher is an acquaintance of Paul, an ophthalmologist who was elected to the Senate in 2010.More news: SC asks father of Kerala woman to produce her on Nov. 27
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The release did not provide details of the assault or the nature of Paul's injury.
Rene Albert Boucher, 59, has been charged with fourth-degree assault with a minor injury, a misdemeanor, according to arrest records.
US Senator Rand Paul made a Wednesday afternoon stop at the UPS Flight Training Center for a roundtable discussion with local business leaders on October 11, 2017.
It's unclear whether the attack against Paul was politically motivated.
CNN was unable to reach a representative of Boucher on Saturday night.