The company has 64.500 employees in 22 countries.
Data exfiltrated from the company has been posted on the Nefilim website on the dark web, with the attackers saying this was the first part of the release.
The Berlin-based company also has operations in Italy, Switzerland, Romania, Hungary, Poland, Luxembourg, Austria, Lithuania, Saudi Arabia, the United Arab Emirates and Vietnam.
A screenshot from the Nefilim site on the dark web announcing the attack on the Dussmann Group.
A Dussmann spokesperson responded to iTWire's request for comment on Thursday, saying a subsidiary of the group had been the target of the attack.
"The refrigeration specialist, Dresdner Kühlanlagenbau (DKA) with 570 employees, has been the target of a cyber attack during which data was encrypted and copied," the spokesperson said.
"DKA is a subsidiary of the Dussmann Group. The servers were shut down as a precaution. The data protection authorities and the State Office of Criminal Investigation in Saxony have been informed and charges have been filed."
The spokesperson said DKA was in close communication with the authorities and external cyber-security experts.
"Operational processes in the business unit for refrigeration air-conditioning plant engineering are secure. DKA has already informed clients and employees about the cyber attack and the data outflow. Due to ongoing investigations, we cannot say more at present," the spokesperson added.