You need to tune up the engine,your spark plugs might gone bad or it could be those small cushions that the engine sits on(I don't know the term really)...
Why Does My Car Vibrate When It's In The Idle State?
This trouble is known as rough idling.It can be of various situations,can be because of bad plugs,broken ignition lead,blocked injector or broken engine mounts.Since you have stated of an engine check light. I assume your vehicle is a EFI one.My advice is to tune up engine first and then check your engine mounts if it stays on.