"An attack on maintenance interfaces is currently taking place worldwide," Deutsche Telecom said in a statement. "This was also confirmed by the Federal Office for Information Security."
The company's network has not been affected by the attack but around 900,000 customers' routers experienced problems, it said.
"We are currently investigating exactly which routers are affected," it said. "There is no error pattern: some customers are experiencing temporary problems or very marked fluctuations in quality, but there are also customers for whom the service is not working at all. Based on the error pattern, we cannot exclude the possibility that the routers have been targeted by external parties with the result that they can no longer register on the network."
Cybersecurity expert Ian Birdsey of Pinsent Masons, the law firm behind Out-Law.com, said: "Telecoms companies make popular targets for cyber attacks. TalkTalk has recently been fined by the UK's Information Commissioner's Office (ICO) over a major data breach last year."
The ICO fined TalkTalk £400,000 in October, in relation to a cyber attack in which the personal data of approximately 157,000 customers was compromised.
"The Deutsche Telekom case is particularly interesting due to the very public nature of the attack, where individual customers' routers are affected," Birdsey said. "Deutsche Telekom has said, however, that there is no evidence that any customer data has been stolen in this case."
Deutsche Telekom said customers affected by the attack should disconnect their router from the power supply and reboot, at which point new software will be downloaded. They can be reassured that there is no permanent infection in their router, it said.
Customers with Deutsche Telekom mobile contracts can also get a pass from one of the company's shops allowing them to access the internet via the mobile network, according to the company.