By Agence France-Presse
Around 900,000 customers using specific models of router have been affected since Sunday afternoon, the firm said, with some unable to connect at all while others suffered intermittent problems.
"We believe that influence was exerted on the routers from outside," a Telekom spokesman told AFP, saying software had been installed on the devices that prevented them from connecting to the company's network.
It did not provide details of which models of router -- network hardware that connects households to their internet and telephone service provider -- were affected.
Deutsche Telekom said that its engineers and colleagues from the companies that produce the devices had been working through the night to find a solution.
Customers affected have been advised to disconnect their routers from the network since the problems began on Sunday afternoon.
Germany has been the target of repeated cyber attacks in recent years.
In September, several political parties were targeted with fake emails purporting to be from Nato headquarters but which in fact contained a link that installed spying software on victims' computers.
Meanwhile, hackers targeted the Bundestag (German parliament) in a 2015 attack that security services have since blamed on Russia.
With federal elections slated for autumn 2017, Germany has anxiously eyed the impact of leaked documents obtained by hackers on the US presidential polls this year.
US authorities have accused Russia of orchestrating the leak of emails from the Democratic National Committee that embarrassed candidate Hillary Clinton.
A cyber attack in October also made large portions of the US internet unavailable for millions of users worldwide.