This sort of constitutional challenge would sound in Due Process. (David Super speculates about this question at Balkinzation). Even the most ardent critic of substantive due process would agree that forcing people to put something on, or in their body, triggers heightened scrutiny.

Would a constitutional challenge to a mask-mandate challenge be viable? Under Jacobson v. Massachusetts the answer is no. Is Jacobson consistent with a century of Due Process Clause jurisprudence? No. Several judges have already begun to cast doubt on that precedent.

This issue is largely academic for now because the mask-mandates are not actually being enforced. I am not aware of the states fining or arresting people who refuse to wear masks. The rubber will meet the road when states begin to mandate vaccinations to develop herd immunity to COVID-19. Courts will be happy to rely on Jacobson.