Irsay was picked up by police on March 17 for allegedly operating a vehicle while intoxicated, while officers also found $29,000 (£17,230) in cash and bottles of prescription drugs in his vehicle.
He will now face one charge of operating a vehicle while intoxicated and one count of operating a vehicle with a schedule I or II controlled substance or its metabolite in the body, both of which could result in a 60-day jail sentence if Irsay is convicted.
"We want to thank the Hamilton County Prosecutor's Office for its professionalism in its investigation regarding Mr Irsay and for devoting the necessary care and attention to determine the facts in this matter did not warrant the filing of felony charges relative to Mr Irsay's prescription medications," read a statement from Irsay's legal team.
"Mr Irsay will deal with the remaining misdemeanor charges through the judicial process."
Irsay entered himself into a rehabilitation facility following the alleged incident.