A broad range of studies demonstrate that sleep has a facilitating role in memory consolidation (see Rasch & Born, 2013). Whether sleep-dependent memory consolidation is also apparent in infants in their first few months of life has not been investigated. We demonstrate that 3-month-old infants only remember a cartoon face approximately 1.5-2 hours after its first presentation when a period of sleep followed learning. Furthermore, habituation time, that is, the time to become bored with a stimulus shown repetitively, correlated negatively with the density of infant sleep spindles, implying that processing speed is linked to specific electroencephalographic components of sleep. Our findings show that without a short period of sleep infants have problems remembering a newly seen face, that sleep enhances memory consolidation from a very early age, highlighting the importance of napping in infancy, and that infant sleep spindles may be associated with some aspects of cognitive ability.