1570s, "insert (a name) in a register or official list," especially "to admit (a student) to a college by enrolling his name on the register," from Late Latin matriculatus, past participle of matriculare "to register," from Latin mÄtricula "public register," diminutive of mÄtrix (genitive mÄtricis) "list, roll," also "sources, womb" (see matrix).
The connection of senses in the Latin word seems to be via confusion of Greek mÄ“tra "womb" (from mÄ“tÄ“r "mother;" see mother (n.1)) and an identical but different Greek word mÄ“tra meaning "register, lot" (see meter (n.2)). Evidently Latin mÄtrix was used to translate both, though it originally shared meaning with only one.
Intransitive sense of "to be entered as a member of a university or college, to become a member of a body or society" is by 1851. Also from late 16c. in English as "to adopt as a child; to naturalize," from the other sense of the Latin word, but these meanings now are obsolete. A list or register of persons belonging to an order, society, etc. was a matricula (1550s), from a diminutive of Latin mÄtrix. Related: Matriculated; matriculating.