Two other boats that also approached Marjan managed to escape after the Saudi navy fired warning shots, the agency reported.
The three guards "are now being questioned by Saudi authorities", the information and culture ministry said in its statement. The Saudi version of the story presents them all as Iranian Revolutionary Guard.
Aghababaie said "even if the boats had entered Saudi waters, the coastguard were not authorised to open fire".
The statement, however, did not say who was behind the attack.More news: Scalise Shooting Suspect Campaigned for Bernie Sanders
The ministry said the boat's cargo had made it "clear this was meant to be a terrorist act in Saudi territorial waters created to cause severe damage to people and property".
The Saudi navy seized a boat carrying weapons as it approached the Kingdom's offshore Marjan oilfield in the Gulf on Friday evening, the official Saudi Press Agency reported on Monday.
"There is no evidence that they are military personnel", ILNA news agency quoted Aghababaie as saying.More news: Sen. Kamala Harris: Not backing down is in ex-prosecutor's DNA
The Foreign Ministry spokesman said the Saudi coast guard's move to shoot and kill an Iranian fisherman was illegal and devoid of any justification.
On Sunday, Iran has launched six ballistic missiles into Syria, targeting positions of Islamic State (IS, formerly ISIS/ISIL) terrorists in retaliation for the twin attacks in Tehran earlier this month.
Iran said it was investigating the Saturday shooting, after two fishing boats may have strayed into Saudi waters.
Saudi Arabia said Monday it had disrupted an attack on an offshore oil field.More news: Kiwis back to challenge United States in America's Cup