Bill Gwatney, a former state legislator, was shot three times by a single gunman, The New York Times reported.
The gunman reportedly entered the party headquarters in Little Rock, asked to speak with Gwatney then fired three shots, Little Rock television station KTHV reported.
Police say a suspect in the shooting was shot and taken into custody after a high-speed chase that ended about 50 miles south of Little Rock.
As a precaution, workers at the nearby Republican Party of Arkansas headquarters were sent home, the television station reported.
U.S. Sen. Mark Pryor, D-Ark., said in a statement he was "sickened" by what happened at the party headquarters.
"Bill Gwatney is an individual who cares a great deal about Arkansas and its future," he said.
Democratic National Committee Chairman Howard Dean called the incident a "senseless tragedy" in a statement.
The Little Rock police, the FBI and the Arkansas State Police were involved in the shooting investigation.