There currently is one option to travel by night train from Amsterdam to Innsbruck, taking approximately 14 hours: Namely the NJ 421 operated by ÖBB.
The Austrian Federal Railways (ÖBB) operate the Nightjet and Euronight trains (the latter together with other national railway agencies). The ÖBB usually offer three types of carriages in their night trains: seats, couchettes, and sleepers. While seats are only for the bravest, couchettes and sleepers offer a more comfortable journey. Couchettes can hold up to six people, whereas sleepers are private compartments for one to three people. They sometimes include a private bathroom or even a shower, sometimes only a sink.
For the next 7 dates with connections, the cheapest offer starts at 55 EUR. Check our connection pages below for all availabilities!