Shuffle by album on iOS-devices?

This is not possible in music.app.

From this Apple Discussion:

The Foobar2000 music player app available in the App Store respects albums and supports 'Shuffle Albums'. It is a competent, comfortable and convenient music player with full Gain Management and many other useful features. It will work with your iTunes library as well as many other music file formats (via iTunes App File Folders). At time of writing it is free.

There are a few apps that can achieve this like Cs Music.

Personally I prefer to use the Shortcuts app (previously Workflow) to queue up random albums and play them back in order. With a lock screen widget or home screen shortcut this can be done with a single tap.

Links to some Shortcuts can be found here, they are quite straightforward to customise if you want to limit to albums within a specific playlist or genre.