The interior and foreign ministries issued a statement about the attack which started shortly before 11.00 pm (2200 GMT) on Saturday.
"Due to the gravity and nature of the attack, it cannot be excluded that it is a targeted attack by a state actor," the statement said.
"In the past, other European countries have been the target of similar attacks.
Immediate measures have been taken and a "coordination committee" set up, the statement said.
The attack came as Austria's Greens on Saturday gave the go-ahead to a coalition with the country's conservatives at a party congress in Salzburg, removing the last obstacle to the unprecedented alliance.
The German government's IT network was hit by a cyber attack in 2018.
Last year the EU adopted powers to punish those outside the bloc who launch cyber attacks that cripple hospitals and banks, sway elections and steal company secrets or funds.