'Shoo' is not 'keep silent', or as Lisa said 'keep quiet'. It is in fact 'go away'. Did you perhaps mean shoosh/shush?

The natural way to say it is "keep quiet". "Keep silent" is grammatically correct, but it sounds a little arrogant. You can write "keep your silence" (ie. with a possessive) but it doesn't make sense as a command. This is probably the example you found in the news.

Keep silence

Shoo is used to tell someone or something to go away. "Shoo! Shoo go away!" To say be quiet or to keep silent you would say Shhh/Shush but shush is more rude than shhh. Shhh can be rude as well though.

'Keep quiet' is not very polite. It is 'bossy'. Maybe you would use it if you were a teacher. It would be better to say 'please be quiet'.