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 mātricula "public register," diminutive of mātrix (genitive mātricis) "list, roll," also "sources, womb" (see matrix).
The connection of senses in the Latin word seems to be via confusion of Greek mētra "womb" (from mētēr "mother;" see mother (n.1)) and an identical but different Greek word mētra meaning "register, lot" (see meter (n.2)). Evidently Latin mātrix 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 mātrix. Related: Matriculated; matriculating.