The Collaborative International Dictionary of English v.0.48:

Jinnee \Jin"nee\, Jinni \Jin"ni\(j[i^]n"n[=e]), n.; pl. Jinn
   (j[i^]n). [Ar.] (Arabian & Mohammedan Myth.)
   A genius or demon; one of the fabled genii, good and evil
   spirits, supposed to be the children of fire, and to have the
   power of assuming various forms. [Written also djinnee,
   genie, etc.]

   Syn: jinn; jin; djinn.
        [1913 Webster]

   Note: Jinn is also used as sing., with pl. jinns.
         [1913 Webster]

WordNet (r) 3.0 (2006):

jinnee
    n 1: (Islam) an invisible spirit mentioned in the Koran and
         believed by Muslims to inhabit the earth and influence
         mankind by appearing in the form of humans or animals [syn:
         genie, jinni, jinnee, djinni, djinny, djinn]