Like humans, dogs, and in particular puppies, can suffer from travel sickness. Whilst they are likely to grow out of this as they mature there are techniques you can use to prevent this becoming a habit.
Start off by putting your puppy in the car and taking it out again. Do this a few times to get them used to going in and out of the car. Once they have got used to this try it again but with the engine turned on. This will help them get used to the noise of the car. Do this a few times until they are comfortable with it.
Once your puppy is used to being in the car with and without the engine turned on, go for a very short drive. If you have a driveway go up and down this in your car, if you don’t then just take a short drive down your street. Repeat this until they are comfortable with the motion of the car. You should then be able to increase the journey length steadily over time.