They said the 42-year-old man is suspected, along with others, of having strung a steel rope across the tracks running between the southern German cities of Munich and Nuremberg, damaging the front window of a high speed ICE train in October last year.
In another case in December last year, cement blocks were put on the tracks. Islamic State (IS) flags and writings in Arabic were found near the crime scenes, Vienna prosecutors said.
They said the group's aim had been to derail trains.
The man was arrested on Monday “under suspicion to have carried out terrorist attacks on railways in Germany in October and December 2018.”
Austrian and German authorities worked together in their investigations leading to Monday's arrest, according to a press release by criminal investigators in Germany's southern state of Bavaria.
Austrian media reported the father-of-five was working at a security company with access to football stadiums.
Germany is on alert following several jihadist attacks in recent years.
The most deadly was committed in 2016 by 23-year-old Tunisian Anis Amri, who killed 12 people when he stole a truck and ploughed it through a Berlin Christmas market.