In British English, schtum is an informal adjective used to mean remaining silent, e.g.:
It's for the best if nobody hears about any of this business, so if you're asked, make sure to keep schtum.
Although I've personally never heard it used as such, according to Oxford Dictionaries.com schtum can also be used as a verb:
Be or become quiet and non-communicative
The definition page provides a few examples, but I think the following is the most apt to the case provided in the question:
The possible risk being that she schtums and won't tell me the truth or just laughs in my face when I bring it up because it's apparently trivial.
This usage in the active voice sounds pretty jarring to my ear, though. Although I'd probably still think it an unusual word-choice, another example taken from Oxford Dictionaries.com utilising the passive voice sounds far more idiomatic:
This source was schtummed when Julia posted a scathing rebuke on the thread, really very angry.
The word schtum on its own can also be used in the imperative/as an interjection:
Used as an imperative, schtum is not directly equivalent to the example of shut-up given in the question (in the sense of an interjectory command for "Silence!"). Its meaning is more akin to "keeping quiet" about something in the sense of not releasing information.