A car engine will shake just running. However, if it is a really bad shake, it could be the engine being out of time, a fouled/misfiring plug (s), a vacuum leak (depending on the year and make of the car), or even trash in the fuel lines going to the carburator/fuel injection system. I'm sure there are others, but these are the most common ones I've found in 40 years of driving and working on cars.
Engine miss.
When the engine light comes on and the car shakes at the same time, it could be the spark plugs or ignition coils are faulty. Misfiring is causing the car to shake.
If your car shakes while underway, your tires have worn incorrectly from misalignment. If it shakes while in park or not moving, your engine is misfiring.
You have a serious problem. Have your car looked at before you drive it.
Could be in need of a tune up.
There is something wrong with it. Or you have one serious engine under the hood
Start checking out your engine and transmission mounts. Check the rubber to make sure it isn't torn.
Do u mean that the car shakes as you are driving, or just that the engine shakes when it is at idle ? Could use more info.
The engine mount (which are made of rubber) are worn out.
Possible cylinder misfire and/or failing engine mounts.
If your engine shakes when you accelerate, you may have a broken motor mount. You need to get it fixed before your engine falls out of your car as you drive along.
If the check engine light is blinking that means an engine cylinder misfire has been detected