Is minister a common noun

Yes, the noun 'minister' is a common noun, a general Word for a member of clergy; a general Word for a head of a government department; a general Word for a government representative in a foreign country.

The noun 'Minister' (capital M) is a proper noun as the title of a specific minister; for example, Prime Minister Justin Trudeau (Canada) or Minister of Health Isaac Folorunso Adewole (Nigeria).