You can do this in the shader node(s) for the object.

In order to make the object completely transparent in the Preview, you will also need to adjust the render setting for Preview transparency. By default, Preview transparency is limited so that you can still see fully transparent objects as semi-transparent in the Preview. Change this setting to Actual and they will disappear completely.

*Edit - the reason why this works is not immediately clear. I can explain if required.

"If I were a shadow, I know I wouldn't like to be half of what I should be."
Mr Otsuka, the old black tomcat in Kafka on the Shore (Haruki Murakami)