The raiders bypassed a complicated system of cameras and sensors to snatch their multi-million euro haul from the Museon, a popular science museum.
"I am shocked. The museum was very well protected with an advanced security system," said museum director Bert Molsbergen.
The gems, including diamonds and other precious stones, had formed the centrepiece of an exhibition on diamonds.
They included a tiara lent to them by the Dutch royal family.
Other exhibits came from private collections and museums around the world.
The museum says it had consulted police about how to secure the diamonds.
As well as 24-hour camera surveillance, the building had special motion sensors installed, and extra security was added to the cases housing the collection.
The diamonds and other gems forming the exhibition centrepiece were housed in 28 cases in a special "treasure chamber".
It was this treasure chamber which was specificially targeted, said museum officials.
Six of the 28 cases in the treasure chamber were smashed, and the highest-value items appear to have been selected.
Owners told
"The private collectors and museums that lent us pieces of jewellery were notified as was the insurance company," said Mr Molsbergen.
The uniqueness of the pieces will make them "practically impossible to sell" he added.
The exhibition, which opened in October, promised visitors the chance to learn about the diamond industry, from mining to finished products.
But it may now have to close, as so many of the key exhibits have gone. It had been due to run until March.