The Collaborative International Dictionary of English v.0.48:

Murmurer \Mur"mur*er\, n.
   One who murmurs.
   [1913 Webster]

WordNet (r) 3.0 (2006):

murmurer
    n 1: a person who speaks softly and indistinctly [syn:
         mutterer, mumbler, murmurer]

Moby Thesaurus II by Grady Ward, 1.0:

23 Moby Thesaurus words for "murmurer":
   bellyacher, complainant, complainer, crab, crank, croaker,
   faultfinder, frondeur, griper, grouch, grouser, growler, grumbler,
   kicker, kvetch, malcontent, mutterer, querulous person,
   reactionary, reactionist, rebel, sorehead, whiner