Attorney General Andy Beshear's office said in a news release that Brown used an online messaging application to communicate with an undercover investigator posing as a minor. Brown asked the undercover investigator to have sexual relations with him.
Officials say Brown traveled to Frankfort to meet the minor and was arrested by investigators there.
Brown said he was a pastor at the First Christian Church of Jeffersonville, Indiana.
It's unclear if he has an attorney.