Cochlear implants (CIs) are optimized for speech perception but poor in conveying musical sound features such as pitch, melody, and timbre. Here, we investigated the early development of discrimination of musical sound features after cochlear implantation. Nine recently implanted CI users (CIre) were tested shortly after switch-on (T1) and approximately 3 months later (T2), using a musical multifeature mismatch negativity (MMN) paradigm, presenting four deviant features (intensity, pitch, timbre, and rhythm), and a three-alternative forced-choice behavioral test. For reference, groups of experienced CI users (CIex; n = 13) and normally hearing (NH) controls (n = 14) underwent the same tests once. We found significant improvement in CIre's neural discrimination of pitch and timbre as marked by increased MMN amplitudes. This was not reflected in the behavioral results. Behaviorally, CIre scored well above chance level at both time points for all features except intensity, but significantly below NH controls for all features except rhythm. Both CI groups scored significantly below NH in behavioral pitch discrimination. No significant difference was found in MMN amplitude between CIex and NH. The results indicate that development of musical discrimination can be detected neurophysiologically early after switch-on. However, to fully take advantage of the sparse information from the implant, a prolonged adaptation period may be required. Behavioral discrimination accuracy was notably high already shortly after implant switch-on, although well below that of NH listeners. This study provides new insight into the early development of music-discrimination abilities in CI users and may have clinical and therapeutic relevance.