Navy spokesman Gig Jonias Mozes Sipasulta said the Vietnamese boats were four nautical miles inside Indonesian territory when intercepted by an Indonesian warship on Sunday.
He denied media reports that four Vietnamese fishermen were injured.
In a statement released last evening, Sipasulta said the two vessels sailed toward the bow of the KRI Wiranto-379, which fired a warning shot, causing the Vietnamese to immediately head for international waters.
Indonesia, the world's largest archipelago with more than 13,000 islands, has become increasingly assertive in defending its maritime territory and exclusive economic zone.
It has destroyed hundreds of foreign fishing vessels caught in its territory and earlier this month said it had renamed the southernmost reaches of the South China Sea as the North Natuna Sea.
Experts said that move was aimed at protecting its exclusive economic zone north of the Natuna island chain, which overlaps with China's nine-dash line that roughly demarcates its claim to the South China Sea.