Does the depo-provera provera (medroxyprogesterone) shot cause movements in your stomach?

No : No it definitely does not.

Depo provera (medroxyprogesterone): Interestingly, progestins (like depo) by virtue of their functions in pregnancy relax smooth muscle. This is beneficial in pregnancy because the uterus is mostly smooth muscle. The muscles that move your bowels also contain smooth muscle so a progestin can change bowel frequency, probably slowing the bowels. I hope this helps- may not be the answer to your question.