"Two fishing boats were in the Persian Gulf and strayed due to high waves. The Saudi coastguard say the boats entered Saudi waters and killed one of the fishermen," Majid Aghababaie, head of border affairs at the interior ministry, said in a statement published by Iranian media.
He said it was not clear if the fishing boats had strayed into Saudi waters and that Iranian authorities were trying to determine the facts.
Foreign ministry spokesman Bahram Ghassemi issued a similar statement.
The shooting comes amid increased tensions between Sunni-led Saudi Arabia and its arch rival Iran.
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The tensions flared after twin attacks on June 7 on the parliament and the shrine of revolutionary leader Ayatollah Ruhollah Khomeini in Tehran in which 17 people were killed.
The Islamic State jihadist group claimed responsibility.
But Iran's elite Revolutionary Guard has accused Saudi Arabia of involvement in the attacks.
Iran's Intelligence Minister Mahmoud Alavi has also put the blame on Riyadh.
Iranian Foreign Minister Mohammad Javad Zarif also pointed the finger at Saudi Arabia, during a visit to Norway this week.
"We have intelligence that Saudi Arabia is actively engaged in promoting terrorist groups operating on the eastern side of Iran in Baluchistan," Zarif said.
The incident also comes as the Gulf faces one of its worst diplomatic crises in years.
Earlier this month Saudi Arabia and several of its allies cut ties with Qatar, accusing it of supporting extremist groups, including some backed by Iran.
Qatar denies the allegations.
It also sent several planeloads of food to Qatar earlier this month after the Gulf countries cut off air links with Doha.
Saudi Arabia also sealed its land border with Qatar, which relies heavily on imports for food and raw materials.