The ministry said the seriousness of the attack suggested it might have been carried out by a “state actor”.
The hack started on Saturday night and experts warn it could continue for several days.
The breach occurred on the same day Austria’s Green party backed forming a coalition with conservatives .
It was recognised very quickly and countermeasures taken immediately, the foreign ministry said in a statement.
“Despite all intensive security measures, there is never 100% protection against cyber-attacks,” the ministry said.
Other European countries have fallen victim to similar attacks in the past.
The German government’s IT network experienced a “very serious” cyber-attack in March 2018.
A Russian group called Fancy Bear was suspected to have been involved and was blamed for a similar attack on the German parliament in 2015.