Odor perception plays a critical role in early human development, but the underlying neural mechanisms are not fully understood. To investigate these, we presented appetitive and aversive odors to infants of both sexes at 1 month of age while recording functional magnetic resonance imaging (fMRI) and nasal airflow data. Infants slept during odor presentation to allow MRI scanning. We found that odors evoke robust fMRI activity in the bilateral olfactory cortex and thalamus and that fMRI response magnitudes in the olfactory cortex differ across odors. However, in contrast to prior work in adults, we did not find compelling evidence that odor stimuli evoke discriminable fMRI activity patterns in the olfactory cortex or thalamus using two different multivariate pattern analysis techniques. Finally, the average inhale airflow rate was higher for appetitive odors than aversive odors, which tentatively suggests that infants could modulate their respiration to reflect odor valence. Overall, these results show strong neural responses to odors at this early developmental stage and highlight nasal airflow as a behavioral metric for assessing odor preference in infants.