The Collaborative International Dictionary of English v.0.48:

Vaishnava \Vaish"na*va\ (v[imac]sh"n[.a]*v[.a]), n. [Skr.
   vaish[.n]ava.] (Hindu Myth.)
   A worshiper of the god Vishnu in any of his incarnations.
   [1913 Webster]

WordNet (r) 3.0 (2006):

Vaishnava
    n 1: worshipper of Vishnu