Prior studies have observed selective neural responses in the adult human auditory cortex to music and speech that cannot be explained by the differing lower-level acoustic properties of these stimuli. Does infant cortex exhibit similarly selective responses to music and speech shortly after birth? To answer this question, we attempted to collect functional magnetic resonance imaging (fMRI) data from 45 sleeping infants (2.0- to 11.9-weeks-old) while they listened to monophonic instrumental lullabies and infant-directed speech produced by a mother. To match acoustic variation between music and speech sounds we (1) recorded music from instruments that had a similar spectral range as female infant-directed speech, (2) used a novel excitation-matching algorithm to match the cochleagrams of music and speech stimuli, and (3) synthesized “model-matched” stimuli that were matched in spectrotemporal modulation statistics to (yet perceptually distinct from) music or speech. Of the 36 infants we collected usable data from, 19 had significant activations to sounds overall compared to scanner noise. From these infants, we observed a set of voxels in non-primary auditory cortex (NPAC) but not in Heschl’s Gyrus that responded significantly more to music than to each of the other three stimulus types (but not significantly more strongly than to the background scanner noise). In contrast, our planned analyses did not reveal voxels in NPAC that responded more to speech than to model-matched speech, although other unplanned analyses did. These preliminary findings suggest that music selectivity arises within the first month of life.