The incident happened at about 8:30 pm on Friday when three small boats entered Saudi territorial waters and "headed at speed towards platforms of (the) Saudi oil field of Marjan", a government statement said.
Saudi naval forces fired warning shots and captured one of the vessels but two escaped, the statement added.
The seized craft was "loaded with weapons for subversive purposes", it said, but gave no details.
The statement said the boats carried "red and white flags".
Iran, which lies across the Gulf, has a flag of green, white and red stripes.
Saudi Arabia regularly accuses Shiite-dominated Iran of interfering in Middle Eastern countries, and has suggested it is linked to instability in the kingdom's east, where minority Shiites live.
Riyadh, the UAE, Egypt and others severed diplomatic and economic ties with Qatar two weeks ago, accusing Doha of supporting groups, including some backed by Iran, "that aim to destabilise the region".
Qatar denies any such support for extremists.
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