It was taken during the night from the Bode Museum in Berlin.
It is not clear how the thieves evaded the alarm system or carried the heavy, half-metre (20.9 in) coin away.
The theft is believed to have happened at around 03:30 Monday morning (01:30 GMT).
The coin is thought to be too heavy for a single person to carry, and police believe the thieves entered through a window. A ladder was found on the train tracks nearby.
“Based on the information we have so far we believe that the thief, maybe thieves, broke open a window in the back of the museum next to the railway tracks,” police spokesman Winfrid Wenzel told Reuters news agency. “They then managed to enter the building and went to the coin exhibition.”
Source: BBC News