The Baltic Ace, a car carrier sailing under a Bahamas flag, collided with the Corvus J, a container ship from Cyprus, on Wednesday, 50 nautical miles from Rotterdam port in a major shipping lane.
The coastguard said 13 people have already been rescued, but that the search was being hampered by strong winds and snow which limited visibility.
"The chance of finding any survivors is very slim because of the very low temperatures but we are still hoping," said a coastguard official.
"The ship is completely under water and we are now trying to locate its position."
The cause of the collision was unclear, but the British Met Office had predicted gale-force winds and rain in the area.
The Baltic Ace was en route from Zeebrugge in Belgium to Kotka in Finland, while the Corvus J was going from Grangemouth in Scotland to Antwerp, Belgium.
Stamco Ship Management Co. Ltd, based in Piraeus, Greece, said it managed the Baltic Ace and that the ship was owned by Isle of Man-based Ray Car Carriers.
Stamco said the ship was carrying cars produced by a Japanese manufacturer but could not give further details.
Ray Car Carriers declined to comment when contacted by Reuters, and Zeebrugge Port declined to give details of the Baltic Ace's cargo, citing confidentiality agreements.
Zeebrugge is the world's leading port for handling new cars and other roll on roll off freight, according to its website. A spokeswoman said about 10 different car brands are routinely loaded onto ships at the port.
SMIT, which is owned by Dutch group Royal Boskalis Westminster and is one of the world's leading salvage firms, said it was too early to say whether the Baltic Ace could be salvaged.
SMIT salvaged the Tricolor, a ship which was carrying nearly 3,000 cars when it sank in the English Channel in December 2002, in an operation that cost about $50 million.
The coastguard said the Corvus J was still in the area and was not badly damaged in the collision. Shipping traffic was not disrupted, the official said, saying it was unclear whether there was any risk of fuel leaks from the sunken cargo ship.
Operations at Rotterdam Port were not affected by the collision, a port spokesman said late on Wednesday.
Rotterdam is Europe's biggest port and handles commodities and manufactured goods.