My car vibrates at idle but smooths out when I start driving

This has been bugging me for a few weeks now. When I am stopped at a red light, the steering wheel and seat have this subtle vibration, almost like a mild massage. But the moment I hit the gas and get moving, everything feels perfectly normal and smooth. I cleaned my throttle body thinking it might be carbon buildup, but no change. I have been reading about the common signs of vehicle trouble to see if this points to engine mounts or maybe just dirty fuel injectors. I also came across a helpful article about the signs you need to visit a car workshop in Al Quoz that mentioned vibrations as something not to ignore. Has anyone solved a shaky idle with a simple fix, or am I looking at replacing motor mounts?