ministeryoudaoicibaDictYouDict[minister 词源字典]
minister: [13] Etymologically, a minister is a person of ‘lower’ status, a ‘servant’. The word goes back via Old French ministre to Latin minister ‘servant, attendant’, which was derived from minus ‘less’. It retained this meaning when it arrived in English, and indeed it still survives in the verb minister. But already by the Middle Ages a specialized application to a ‘church functionary’ had developed, and in the 16th century this hardened into the present-day ‘clergyman’.

The political sense of the word developed in the 17th century, from the notion of a ‘servant’ of the crown. Derivatives from other languages to have established themselves in English include métier [18], which came via French from Vulgar Latin *misterium, an alteration of Latin ministerium ‘service’ (source of English ministry [14]), and minstrel.

And etymologically, minister is the antonym of master, whose Latin ancestor was based on magis ‘more’.
=> métier, minstrel, minus[minister etymology, minister origin, 英语词源]
minister (v.)youdaoicibaDictYouDict
early 14c., "to perform religious rites, provide religious services;" mid-14c., "to serve (food or drink);" late 14c. "render service or aid," from Old French menistrer "to serve, be of service, administer, attend, wait on," and directly from Latin ministrare "to serve, attend, wait upon" (see minister (n.)). Related: Ministered; ministering.
minister (n.)youdaoicibaDictYouDict
c. 1300, "one who acts upon the authority of another," from Old French menistre "servant, valet, member of a household staff, administrator, musician, minstrel" (12c.), from Latin minister (genitive ministri) "inferior, servant, priest's assistant" (in Medieval Latin, "priest"), from minus, minor "less," hence "subordinate," (see minus) + comparative suffix *-teros. Formed on model of magister. Meaning "priest" is attested in English from early 14c. Political sense of "high officer of the state" is attested from 1620s, from notion of "service to the crown."