The thieves broke into the Green Vault at Dresden's Royal Palace -- home to around 4,000 precious objects made of ivory, gold, silver and jewels -- after a power cut deactivated the alarm at dawn Monday.
Security camera footage showed two men breaking in through a grilled window, police said.
The alarm sounded just before 5 a.m. local time (0359 GMT) and officers were there five minutes later. But the burglars had escaped, Presstv Reported.
The stolen items included three "priceless" sets of diamonds, the director of Dresden's state art collections Marion Ackermann told reporters at a press conference on Monday.
Ackermann confirmed the sets included brilliant-cut diamonds which belonged to an 18th-century collection of jewelry assembled by the museum's founder.
"We are talking here about items of inestimable art historical and cultural-historical value," she said but declined to give an exact estimate of the financial damages.
"We cannot put an exact value on them because they are priceless."
It would be impossible to sell such unique, identifiable items on the open market, added Ackermann.
"It would be a terrible thing," she said when asked whether the jewelry might be broken up or melted down. Its cultural value far outstripped any material value, she added.
The haul was worth up to 1 billion euros ($1.1 billion), Bild newspaper reported earlier, without giving a source.
Dirk Syndram, another director at the museum, said the sets amounted to "a kind of world heritage," totaling about 100 jewelry items.
At dawn on Monday, a fire had broken out at an electrical panel nearby, deactivating the museum's alarm as well as street lighting, police said, adding that the investigations were ongoing to determine if there was a link to the robbery.
Despite the power cut, a surveillance camera kept working and filmed two men breaking in.
"Two suspects can be seen on the recordings, but that doesn't mean there weren't other accomplices," said Volker Lange of Dresden's police force.
Founded by Augustus the Strong, Elector of Saxony in 1723, the Green Vault is one of 12 museums which make up the famous Dresden State Art Collections.
The museum is now made up of two sections -- a historic part and a new part.
And its historic section, which contains around three-quarters of the museum's treasures, was the one broken into on Monday.
With a strict limit on the number of daily visitors, entrance to the historic vault can only be reserved in advance.
Exhibits are arranged into nine rooms, including an ivory room, a silver gilt room and the central "Hall of Treasures."
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.
Other exhibits in Dresden include a table-sized sculpture of an Indian royal court, made out of gold, silver, enamel, precious stones and pearls.
Another is a 1701 golden coffee service by court jeweler Johann Melchior Dinglinger, decorated with lounging cherubs.
The treasures of the Green Vault survived Allied bombing raids in World War Two, only to be carted off as war booty by the Soviet Union.
They were returned to Dresden, the historic capital of the state of Saxony, in 1958.
The theft was a blow to the whole state, its premier, Michael Kretschmer, said.
"The works in the Green Vault and the Palace were built up by the people of Saxony with many centuries of hard work," he said.
"One cannot understand the history of our country, our state without the Green Vault and Saxony's State Art Collections."
Monday's theft is the second high-profile heist in Germany in recent years, after a 100-kilogram (220-pound), 24-carat giant gold coin was stolen from Berlin's Bode Museum in 2017.