Sensual massage in Innsbruck is usually a part of the local brothel and sex club scene. LaJoya at Trientlgasse 65 and Shiva Institute (https://www.shiva-institut.com/) at Valiergasse 61 are two studios in Innsbruck which are specialized in erotic massage (erotische Massage in German). There are some Asian spots here and there, but nothing big.
Also you can find plenty of online ads of freelance (erotic) masseuses on Massagen (https://www.massagen.at/) and Ladies (https://www.ladies.de/). It’s quite cheap too. You can get already a decent rub and tug in Innsbruck for €50.