The infant brain shows rapid neural network development that considerably influences cognitive and behavioral abilities in later life. Reportedly, this neural development process can be indexed by estimating neural signal complexity. However, the precise developmental trajectory of brain signal complexity during infancy remains elusive. This study was conducted to ascertain the trajectory of magnetoencephalography (MEG) signal complexity from 2 months to 3 years of age in five infants using multiscale entropy (MSE), which captures signal complexity at multiple temporal scales. Analyses revealed scale-dependent developmental trajectories. Specifically, signal complexity predominantly increased from 5 to 15 months of age at higher temporal scales, whereas the complexity at lower temporal scales was constant across age, except in one infant who showed decreased complexity. Despite a small sample size limiting this study's power, this is the first report of a longitudinal investigation of changes in brain signal complexity during early infancy and is unique in its application of MSE analysis of longitudinal MEG data during infancy. The results of this pilot study may serve to further our understanding of the longitudinal changes in the neural dynamics of the developing infant brain.