The stolen jewellery is "unique in Europe", said Dirk Syndram, the director of the Grunes Gewolbe.
"We can not put an exact value on them because they are priceless", said Ackermann, adding she was "shocked by the brutality of the break-in". The responsible energy supplier confirmed the incident and said it was investigating if the two events were linked.
Security camera video showed two men breaking in through a grilled window, police said, according to Reuters.
Police sealed off the constructing in Dresden's Baroque metropolis palace and stated they had been nonetheless attempting to work out what was lacking.
Dresden's State Art Collections director, Marion Ackermann, said it was impossible to estimate the value of the items.
He explained that the stolen sets were part of a 10-set collection which included not only diamonds, but also sapphires, rubies and emeralds.
The collection was founded in the 18th century by Augustus the Strong, Elector of Saxony and later King of Poland, who commissioned ever more brilliant jewellery as part of his rivalry with France's King Louis XIV.
One of its best known treasures - the 41-carat Dresden "Green Diamond" - was away on loan to New York's Metropolitan Museum of Art at the time of the break-in.
And its historic section, which contains around three-quarters of the museum's treasures, was the one broken into on Monday.
There are about 3000 items of jewellery and other treasures decorated with gold, silver, ivory and pearl.
Seventeen objects from the museum are now on loan to New York's Metropolitan Museum of Art, including one of its best known pieces, a hat ornament featuring the 41-carat Dresden Green Diamond.
The entrance to catacombs under the August Bridge, where a fire destroyed the power supply for the State Art Collection with the Green Vault.
"This is a bitter day for the cultural heritage of Saxony", he said.
Michael Kretschmer, the regional prime minister, described the robbery as a crime against the Saxon people. One of the most iconic and prized pieces of the collection, the 41-carat Dresden 'Green Diamond, ' is now on loan to New York's Metropolitan Museum of Art and thus escaped any threat from Monday's heist.
In 2010, the museum hosted a meeting between Chancellor Angela Merkel and then President of the United States Barack Obama, on the latter's first state visit to Germany.