The hacker group going by the name of Rex Mundi said they hacked into the servers of Domino's Pizza France and Belgium.
The hackers have managed to download more than 592,000 customer records from Dominos France and 58,000 records from Belgian website.
They claim the compromised database contained sensitive information such as customer's full names, addresses, phone numbers, delivery instructions, email IDs and passwords.
The group gave a deadline of 8PM CET for Dominos to pay them.
"If they do not do so, we will post the entirety of the data in our possession on the Internet." The group said.
Domino's France posted a series of tweets in which it acknowledged the hack and recommended users to change their passwords.