If its shaking side to side could be a tire out of balance or maybe a mechanical issue (wheel bearing, alignment, etc). Probably not a safety issue, but it can wear the tires out prematurely which can be expensive. Warped brake rotors are the most likely cause if the steering wheel only shakes when applying the brakes.
Tires need to be balanced and re-aligned
The tires are out of balance...may need tires, or rim(s) are bent
Seat Steering Wheel Mirror Tires Radio Brakes
Normally this is caused by one or more of the tires out of balance. If the steering wheel is shaking then you know it is a front tire. Have all your tires rotated and balanced.
This is a classic symptom of a tire out of balance. Have the tires inspected for damage and have the tires rotated and balanced. This should solve the problem.
You most likely need to tires for the front of your car. You should replace your tires as soon as possible.
It may be from tires being worn unevenly and off balance or the front end is out of alignment.
Are your tires balanced? I'd check that first.
Wheel Bearings are most likely worn.
More than likely your tires are out of balance. Have your tires rotated and balanced. Make sure they check for a bent wheel.
You probably need to get your tires balanced. Or replaced. If the bias goes (steel belt breaks or shifts), the car will waddle at low speeds, and the steering wheel will shake at high speeds.