Not really, or better it depends on the country. Here, for instance, citing the constitution:
Art. 32: The Republic safeguards health as a fundamental right of the individual and as a collective interest, and guarantees free medical care to the indigent. No one may be obliged to undergo any health treatment except under the provisions of the law. The law may not under any circumstances violate the limits imposed by respect for the human person.
Other vaccines have already been mandated, here and elsewhere. In the U.S. specifically, there is a Supreme Court case in 1905 (Jacobson v. Massachusetts) where the court said that states have under their police powers, which is under the Constitution, the authority to enact reasonable regulations as necessary to protect public health, public safety, and the common good. Vaccination mandates constitute exactly that kind of permissible state action to protect the public's health:
The rights of the individual may at times, under the pressure of great dangers, be subjected to such restraint to be enforced by reasonable regulations as the safety of the general public may demand.
So I think in the end it could be enforced also over there. Without mentioning possible alternative routes such as private businesses requiring proofs of vaccination before providing services.
