How to stop getting sick playing Minecraft Xbox 360 Editition?

Put ot on un-sick mode! Come on dude, don't tell me you didn't know there was an un-sick mode. Its in -> setting -> others -> youjustgottrolledback

I googled it for you and came up with a few solutions:
1) You could try downloading a texture pack to see if it relieves your sickness.

2) I'm not 100% (I'm about 50%) sure but I think it's down to field of view. The smaller the field of view the higher the potency of motion sickness.

Try finding a mod to change the field of view, I'm sure they are out there. There's a way to change it in TF2 so I'm sure there will be a way for minecraft.

3) Field of View was my first thought as well. Most games have it set somewhere between 75 and 110, which is quite a wide range.

4) It may also be a framerate issue, I'd suggest lowering some of Minecraft's graphics options to see if it runs smoother and helps with your problems.

Some people get motion sickness from first-person games like Minecraft. Motion sickness is caused by your brain getting conflicting signals from you eyes and inner ear (used for balance.) When you play a first person game, your eyes think you should be moving but your inner ear knows you aren't actually moving. This conflict can cause dizziness or nausea.

You can try a few things:
1: Sit further from the screen.
2: Only play in a brightly lit room.
3: Take frequent breaks (every 20-30 minutes) where you look at something else, or even get up and walk around a bit.

You can try nibbling on some candied ginger for the nausea. Ginger helps with a variety of tummy problems, including nausea. However I wouldn't rely on this just so you can play Minecraft (or other first person games) as too much ginger can upset your stomach.