None of the crew members was injured, rescue officials said.
The coastguard received a distress signal from the boat just before midnight and dispatched rescue vessels and a helicopter to the scene.
The crew was eventually transported to a rescue vessel, which tried to tow the German boat, but the attempt was unsuccessful and the sailboat sank.
"This appears to have happened so quickly that the people seem to have just gotten out of their berths and up on deck," Oddur Halldorsson, captain of the rescue vessel, told online newspaper Visir.
The crew was transported to Sandgerdi, a small fishing village in southwestern Iceland, where police and staff from the German embassy met them.