There are many such idioms, not so many proverbs that I can think of.

Maybe the most famous proverb on keeping silent is from Scripture:

>Even a fool, when he holds his peace, is counted wise: and he that shuts his lips is esteemed a man of understanding.

It's repeated in various parts of Scripture in different phrasing. I think it's the basis of the familiar 

> It is better to be silent and be thought a fool, than to speak and remove all doubt.  

The following is attributed to Confucius:

>Silence is a true friend who never betrays. 

In addition to the idioms @Dan Bron mentions, there is also **flying under the radar**, originally meaning avoiding detection, but now meaning avoiding negative attention as well. 

However, even wise people often embrace silence, and there is a saying in teaching that no question is a stupid question. How can one learn if one doesn't ask questions?