A gang of masked thieves broke in to the museum in Wingen-sur-Moder in northeastern France around 5:30 a.m. (3:30 a.m. GMT), forcing a door before heading for the jewellery room and smashing open six display cases, a source close to the investigation told Agence France-Presse (AFP).
"Around 20 pieces of jewellery were stolen. The loss is currently being assessed but could amount to several million euros, likely close to 4 million," the source said.
Another source close to the investigation said the stolen jewellery was crystal, without precious gems, and could not be melted down.
The museum said on its website that it will be closed for several days because of the burglary.
"An alarm went off, but by the time the security company had completed its checks, it was a cleaning lady who arrived first on the scene and called the police," the first investigation source added. The CCTV footage is currently being examined.
The mayor of Wingen-sur-Moder, a town of 1,500 inhabitants about 60 kilometers (37 miles) northwest of Strasbourg, told local newspaper Les Dernieres nouvelles d’Alsace (DNA) he was angry about the burglary.
"All the alarms went off, just as they should. And then with the security company, apparently, there was a major failure on their part: they didn't intervene right away, they didn't inform the gendarmes," Christian Dorschner said.
"They were surely well informed to carry out this job in that way; they must be ... specialists," the mayor also told DNA.
The Lalique museum was seen as a "sensitive" site, receiving special attention in the wake of the dramatic daytime heist at the Louvre museum in Paris in October last year, which put security at French museums and galleries under the spotlight.
Thieves made off with $102 million worth of jewellery, including some of the old French crown jewels, from the Louvre in a raid lasting less than eight minutes.