The technician replaced my 255/55/18 tires with 235/55/18 tires and now my car shakes at high speeds. is this the cause?

No, all that's doing is making your speedometer and odometer inaccurate by 3%. When you read 60 mph on the speedo, you will actually be going only about 58 mph. Similarly, your odometer will be off, everytime you go 100 miles, you will only have gone about 97 miles. Your tire dealer should have actually replaced your 255/55/18's with 235/60/18's instead, because those would have almost identical circumference (off by a mere 0.2% which is nothing).

However, that being said, none of that will affect the shaking at high speeds. That's entirely due to an unbalanced tire, perhaps a balancing weight has broken off the rim? Or perhaps they did a bad job of balancing it. Just go back to the tire place and tell them about it, and that it shaking at high speeds, and to have them rebalance the tires again.

They did NOT balance the tires correctly and MATBE the ones they sold you are SUBSTANDARD and already have SLIPPED BELTS. STICk with MICHELIN< CONTINENTAL and YOKOHAMA and BRIDGESTONES! 

The size isn't, but the tires are either out of balance or have crooked belts.

Go back to the same joint and tell them. They need to balance those tires, which they did not do.  The only difference between the tires is width of the tire. He ain't a tech, he is a tire shop. I always call them the tire guy. Not an insult. It is just a job.

 When he took off the old tires he also takes off the Lead wheel weights that balanced THAT tire.  When a new tire is put on it has to be rebalanced (part of the job) They are the guys that can fix it and where you should start.  Normally they do all 4 wheels because we rotate tires so backs come to the front and front to back.(on radial tires)

no means you have tires unbalanced or need a front end alignment .

you would have to ask a mechanic

Either they are out of balance, a bent rim, or a defective tire

It's not the tire size causing the shaking...it's the tire balancing that wasn't done right. 

No, you have a wheel out of balance. Get them balanced, simple as that.  

Or, possible but unlikely, one of the new tires has a fault.  They'll detect that when doing the balance.

Unless you okay it sounds to me like you have lost one of the balancing weights. That's a little lead weight that balances the tire it either fell off or one of the tires is not properly balanced