If it happens when you are driving fast (60-70 MPH) it could be that your wheels are out of alignment.
have your front tires rebalanced.
One or more tire out of balance, a bent wheel, or defect in a tire.
Tire out of balance, bent wheel, loose or worn suspension parts. More than likely balancing & rotating your tires will correct this.
Check the wheel balance
Probably i would go for wheel balance and maybe check your wheel bearings rotors will not make it shake because of speed
It might be your transmition...
My guess would be wheel balance.
Probably wheel balance but you should have the front end safety checked for your own safety. You may have a tie rod end ready to separate and you would lose your steering, not good.
My minivan did the same thing - it turns out I simply needed the wheels balanced (about 7 bucks per tire). That took care of it. Hope this helps.
possibilityThe car is out of alignment or you have a wheel out of balance.
Struts and alignment This typically happens when the the wheel alignment is off.