The story is quite simple: humanity has been sending out communications via radio waves (possibly) into the depths of space, and after some time of searching, they eventually receive a response from alien life.
The response is along the lines of:
Be quiet. They are listening
After that revelation the story ends.
It is from quite a while ago. I am not sure of the date of publication, but it's definitely a story from the 70s to even the 90s. I thought it could possibly be Asimov, but can't find it under the Wikipedia list of science fiction short stories.