The three "are now being questioned by Saudi authorities," the information and culture ministry said in a statement, at a time of already-heightened tensions with Iran.
"It is clear this was intended to be a terrorist act in Saudi territorial waters designed to cause severe damage to people and property," the ministry said.
The latest statement came more than 12 hours after Saudi Arabia said it had seized weapons from a boat captured in the Gulf's Marjan field at about 8:30 pm Friday.
That statement made no mention of explosives and did not detail what type of weapons were found, though it said they were for "subversive purposes".
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That statement also made no mention of arrests but said the boats bore "red and white flags".
Two of the boats got away, it said.
Yesterday Iran accused the Saudi coastguard of killing one of its fishermen after two fishing boats may have strayed into Saudi waters.