The Russian hacking group Fancy Bear, or APT28, is being widely blamed in the German media. They are thought to be behind some cyber attacks on the West, including breaches in the 2016 US election.
The hack was first realised in December and may have lasted up to a year, the DPA news agency reported. The group is reported to have targeted the federal government's internal communications network with malware.
A German interior ministry spokesman confirmed the Federal Office for Information Security (BSI) and intelligence services are investigating a cyber security incident concerning the federal government's information technology and networks.
He said the attack was "isolated" and had been "brought under control" but declined to comment on reports of Russian involvement.
Fancy Bear was blamed for a similar attack on the lower house of the German parliament in 2015 and is also thought to have targeted the Christian Democratic Union party of Chancellor Angela Merkel.
Officials in the country issued repeated warnings about the potential of "outside manipulation" in last year's German election.
The hacking group has been linked to the Russian state by multiple security experts investigating its international hacks. The group played a crucial role in 2016's attack on the Democratic National Committee (DNC) in the US, according to security experts.