There's nothing quite like the Schwebebahn, but there are a few other suspended monorails out there, also known as SAFEGE monorails after the French company that commercialized the technology. The largest is the Chiba Urban Monorail near Tokyo, which is actually a two-line network:

https://en.wikipedia.org/wiki/Chiba_Urban_Monorail

Pro tip: JR trains from Narita Airport to central Tokyo pass through Chiba station, so you can hop off and go for a suspended monorail ride!