The Collaborative International Dictionary of English v.0.48:

Incommunicable \In`com*mu"ni*ca*ble\, a. [L. incommunicabilis:
   cf. F. incommunicable. See In- not, and Communicable.]
   Not communicable; incapable of being communicated, shared,
   told, or imparted, to others.
   [1913 Webster]

         Health and understanding are incommunicable. --Southey.
   [1913 Webster]

         Those incommunicable relations of the divine love.
                                                  --South.
   -- In`com*mu"ni*ca*ble*ness, n. -- In`com*mu"ni*ca*bly,
   adv.
   [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

18 Moby Thesaurus words for "incommunicable":
   inalienable, indefeasible, indefinable, indescribable, ineffable,
   inenarrable, inexpressible, innominable, noncommunicable,
   noncontagious, noninfectious, undefinable, unimpartable,
   unmentionable, unnameable, unspeakable, unutterable,
   unwhisperable