CORRECTION (Nov. 4, 10:27 p.m.): An earlier version of this article misstated the relationship between Paul and Boucher.
Boucher, 59, was charged with assault and was being held as of Saturday on a $5,000 bond.
"Senator Paul was blindsided and the victim of an assault".
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Congress is also looking into allegations of collusion between Trump associates and Russian Federation . The subpoena is part of the committee's investigation into Russian meddling in the 2016 election.
She added that the Senator was "fine" and the incident is now a matter for police.
The release did not provide details of the assault or the nature of Paul's injury.
"Kelley and I appreciate the overwhelming support after Friday's unfortunate event", Paul tweeted. "Thank you for your thoughts and prayers", Paul said on Twitter on Sunday morning, referring to his wife.
Paul has been Kentucky's junior senator since 2011.
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"They are top and play well with a lot of goals.but we have a lot of games to play, we will see at the end of the season". I am answering very well about these different issues".
However, Boucher is an anesthesiologist and pain specialist in Bowling Green, who developed a product called Therm-a-Vest.
Politico reported, citing the arrest warrant, that Paul was tackled from behind, and that "Boucher's altercation with Paul left the senator having difficulty breathing as a result of a "possible rib injury" in addition to bleeding from cuts around his mouth".
CNN was unable to reach a representative of Boucher on Saturday night.
State Police Master Trooper Jeremy Hodges told The Associated Press that he couldn't reveal any other details of the assault because of security issues.
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It was not clear what motivated the altercation and Paul did not go to the hospital, police said.