The accident happened at around 1:30 am (1130 GMT) when the 32-metre Maria, a ship deployed to guard an oil drilling platform about 40 kilometres (24 miles) southwest of the Dutch navy port of Den Helder, collided with fishing trawler Texel 68.
“We have scrambled two rescue ships and other vessels are looking too, as well as two helicopters,” coast guard spokesman Peter Westenberg told AFP.
He said the Maria, which sank shortly after the collision, had a crew of five on board.
“Two crew members were rescued but the other three are still missing,” he said.
“Their nationalities are unknown at this stage,” he added.
Westenberg said the cause of the crash was unclear.
The most serious recent incident off the busy Dutch coast happened last December when a cargo ship collided with the car-carrier Baltic Ice off the port of Rotterdam, killing 11 sailors.