The most literal analogy would be the hippeis/ἱππεῖς -- horsemen: people wealthy enough to serve the civic militia on as cavalry rather than on foot (supplying their own warhorse). Hippeis were somewhat like Medieval knights in that they were semi-elite socially (although not the top class in society) and that they fought mounted, although they were not like Medieval knights in many other ways: they were still fundamentally militia rather than full-time soldiers, and their tactical importance in battles was much less than that Medieval knights (pre-Macedonian Greek horsemen may have played vital roles in scouting, communication, etc, but they were rarely competitive with hoplite foot-soldiers on the battlefield). Socially, they were also quite different. A Medieval knight was most likely to be bound by personal loyalty to a lord. A Greek hippeis was bound to the city (polis).

Less literal analogies, focused more on institutional/social role rather than a literal translation of "cavalry class," would probably have to go back to the Mycenaean period to find some class with more knight-like attributes (personal loyalty to a lord rather than loyalty to a state, being a full-time soldiers, etc).

Update: Macedonian companion cavalry (hetairoi/ἑταῖροι) also have some parallels with Medieval knights (aristocratic status, full tie mounted soldiers, fairly high tactical importance, personal attachment to a lord), but I think they're more properly regarded as a specific military unit rather than being thought of as a real social class. (They were drawn from a broader aristocratic social class, but that social class as a whole resembles Medieval knights much less than the companions.)