State police earlier said the man has "unknown injuries" after he fled and exchanged gunfire with law enforcement.
An update posted to the Facebook page of the Clinton County Emergency Management Agency indicated the "law enforcement operations and response" was over, but included no information about how the standoff was resolved or the status of the suspect.
Officials said the man was wearing body armor and was chased onto a highway, then had abandoned his car on nearby country roads bordered by woods and farm fields just off I-71, about 45 miles (72 kilometers) northeast of Cincinnati.
The confrontation came as officials warned of an increase in threats against federal agents in the days following a search of former President Donald Trump's Mar-a-Lago estate in Florida.
Federal officials said the man "attempted to breach" the visitor's screening area at the FBI office and fled when agents confronted him. After fleeing onto Interstate 71, he was spotted by a trooper and fired shots as the trooper pursued him, said Lt. Nathan Dennis, a Ohio State Highway Patrol spokesperson.
The suspect left the interstate north of Cincinnati and abandoned his car on rural roads, where he exchanged gunfire with police. The man has "unknown injuries," but no one else was hurt, the patrol said.
State highway workers blocked off roads leading to the scene as a helicopter flew over the area. Officials locked down a mile radius near the interstate and urged residents and business owners to lock doors and stay inside. The interstate has been reopened.
There have been growing threats in recent days against FBI agents and offices across the country since federal agents executed a search warrant at Mar-a-Lago. On Gab, a social media site popular with white supremacists and antisemites, users have warned they are preparing for an armed revolution.
Federal officials have also been tracking an array of other concerning chatter on Gab and other platforms threatening violence against federal agents. FBI Director Christopher Wray denounced the threats as he visited another FBI office in Nebraska on Wednesday.
"Violence against law enforcement is not the answer, no matter who you're upset with," Wray said Wednesday in Omaha.
The FBI on Wednesday also warned its agents to avoid protesters and ensure their security key cards are "not visible outside FBI space," citing an increase in social media threats to bureau personnel and facilities. It also warned agents to be aware of their surroundings and potential protesters.
The warning did not specifically mention this week's search of Mar-a-Lago but attributed the online threats to "recent media reporting on FBI investigative activity."