It is true that cures from disease lie in the hands of Allah but it is recommended to seek a treatment, as evidenced by the words of the Prophet who said, "O servants of Allah! Seek treatment because Allah did not make a disease without making a cure for it except for old age" [Recorded by al-Hamidi].

If the ruler mandates vaccinations, such as polio vaccinations and the like, as a preventive measure against diseases, it is then incumbent upon every person to obey him. This is because Islamic law entitles a ruler to restrict the permissible and command the recommended, so as to make them obligatory, to achieve those interests he deems important.

The ruling
Based on this, it is impermissible and legally blameworthy for a person to contradict the ruler's orders—the obedience of which are obligatory—with the excuse that Allah is the Healer and that seeking a cure is merely recommended.
Allah Almighty knows best.