The ships, Polesie and Verity, crashed about 22km south-west of the island at about 5am on Tuesday, the German Central Command for Maritime Emergencies said.
One of them, the British-flagged Verity, is believed to have sunk. It was carrying steel, according to a spokesman for its owner, Faversham Ships.
The German Central Command said one body had been recovered and two people rescued in a search.
Seven were on board the Verity, it said in a statement, and added that the search for those still missing was continuing.
“We are now doing everything humanly possible to rescue more people alive,” the head of the emergency command, Robby Renner, said at a news conference in Cuxhaven.
A signal from the ship was lost at about 5.20am, suggesting that it had already gone down, and wreckage was found.
“The central command assumes that the Verity sank due to the incident,” the statement said.
“It was possible to rescue one person from the water and they are receiving medical attention. Several other people are currently missing.”
The water temperature at the time of the accident was about 12°C, which humans can survive for about 20 hours, said Michael Ippich of the German Maritime Search and Rescue Service.
“The conditions on the spot are extremely difficult,” he said. “Because of the weather and visibility under water, it's incredibly difficult to conduct such an operation.”
Several rescue ships and aircraft taking part in the search had not located the missing crew members by midafternoon.
Rescuers were considering the possibility that they were still inside the Verity, and planned to send divers down to the wreck at a depth of about 30 metres to check for signs of life.
“The emergency services are doing everything they can to rescue the missing people,” German Transport Minister Volker Wissing said.
“My thoughts are with the crew members, their relatives and the rescue teams who have been in action since early this morning.”
Two rescue cruisers, an emergency tug, a pilot boat, a police patrol boat and a helicopter are helping with the search.
The P&O cruise ship Iona, which is in the area, has also been involved. It has doctors on board and could treat people if needed, the emergency command said.
More medical personnel are being taken to the scene by helicopter.
The search is taking place in difficult conditions, with winds of more than 40kph and waves reaching as high as three metres, the agency said.
Verity was headed from Bremen, Germany, to the English port of Immingham.
The other ship, the Bahamas-flagged Polesie, which was travelling from Hamburg to La Coruna in Spain, remained afloat with 22 people on board.
The Verity is about 900 metres long and can carry 3,360 tonnes of cargo, fuel, crew and other materials. It was previously assisted by UK and Netherlands rescue teams after its engine failed off the coast of Devon in February 2016, according to Vessel Finder. At that time it had a crew of seven sailors.
The Polesie is double the length and has about 10 times the carrying capacity compared to the smaller ship, according to the website Vessel Finder.
The accident comes weeks after a ship with hundreds of electric cars on board caught fire in the North Sea off the coast of the Netherlands.
The Fremantle Highway was sailing between Bremerhaven in Germany and Port Said in Egypt when the blaze broke out in July.
The accident occurred close to Ameland, part of an archipelago of ecologically sensitive islands situated in the Waddenzee area.
One person died and several were injured.
Efforts to tow the ship to shore were complicated by poor weather but it was eventually brought to the northern port of Eemshaven.