Hamed Sedaqati, 29, went missing three days ago in the restive Sistan-Baluchestan province, home to a large Sunni minority.
The area has been the scene of armed conflict in recent years with extremists carrying out assassinations, bombings and kidnappings targeting Iranian officials and civilians.
Sedaqati, who won a bronze medal in the 2006 Asian Games, was travelling with two men towards Khash, a town 1,240 kilometres (770 miles) southeast of Tehran.
Interior Ministry spokesman Rouhollah Jomei told the official IRNA news agency that "no concrete, official or clear motives" have been found for the kidnapping of Sedaqati, which occurred Wednesday night.
But he did not rule out a "personal vendetta" against Sedaqati or his two companions: Mehdi Hosseini, a lawyer, and Mohammad Ali Ghafari, who was fatally shot five times in the chest, according to media reports.
The kidnapping comes three months after five Iranian border troops were abducted by extremist Sunnis while participating in mandatory military service in Sistan-Baluchestan.
Four of the soldiers were eventually freed and returned home in April. Officials say the fate of the fifth soldier is unknown, but he is assumed dead.
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