Mine does this too and does it even when stopped. You can also very faintly feel the vibration in the shifter when it happens.
I am going to visit my parents very soon and my dad is the service manager of a Chevy dealer (and previous to that, master, ASE certified mechanic). He is going to check it out for me and obviously, he's going to be wanting to err on the side of fixing it for me
I will let you all know what he finds when he checks it out.