* Hold your tongue: This is a very similar idiom that directly translates to "keep your mouth shut" and emphasizes the act of not speaking.
* Keep your mouth shut: This is a more direct and forceful idiom that implies silence is mandatory.
* Zip it: This is a more informal and playful idiom that suggests a quick and complete closure of the mouth.
* Button your lip: This is a slightly archaic idiom but still used occasionally, implying a need to be quiet and discreet.
* Keep it under your hat: This idiom emphasizes secrecy and the need to not share information.
* Swallow your words: This idiom implies a regretful silence after already speaking.
The best idiom to use depends on the context and the desired level of formality.