Around 900,000 routers across Germany were hit by the outage which started on Sunday, a company spokesman told DPA on Monday.
The routers connect customers not only to the internet, but also to telephone and television services. The spokesman explained that the problem was not with the network itself, but rather with identifying routers upon dial-up.
The company is now looking into evidence found by IT analysts that the connection problem may have been due to an outside attack rather than a normal system failure, Telekom said late Monday morning.
"We have found the first indications that we were possibly victims of a hacker attack," a spokesman said.
The company said it was introducing a new software on Monday morning that they expected would remedy the problem, after clients - including The Local - could still not connect when the day started.
What to do if your internet is down
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.