The Collaborative International Dictionary of English v.0.48:

Miff \Miff\ (m[i^]f), n. [Cf. Prov. G. muff sullenness,
   sulkiness, muffen to be silky, muff["i]g sullen, pouting.]
   A petty falling out; a tiff; a quarrel; offense. --Fielding.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Miff \Miff\, v. t.
   To offend slightly. [Colloq.]
   [1913 Webster]

WordNet (r) 3.0 (2006):

miff
    n 1: a state of irritation or annoyance [syn: huff, miff,
         seeing red]
    v 1: cause to be annoyed; "His behavior really miffed me"