Cerebral asymmetry is a cardinal feature of functional organization in the human brain and an important biomarker of successful brain development. Studies have demonstrated that functional network asymmetries across hemispheres undergo significant development through childhood and adulthood. However, it remains unknown when such asymmetries of functional networks emerge and how they develop across the early months of infancy. To address this issue, we used multiple-channel functional near-infrared spectroscopy (fNIRS) imaging to record spontaneous brain activity in 66 healthy infants aged 3–9 months. We then adopted a graph-theory analysis approach to quantify the topological characteristics of hemispheric networks in each participant. Our results showed that infants aged 3 to 6 months old exhibited leftward asymmetries in local network efficiency, while infants aged 6 to 9 months old exhibited leftward asymmetries in global network efficiency. Importantly, the degree of leftward asymmetry in global network efficiency was increased over development from 3 to 9 months old, with a faster increase in the left hemisphere than in the right hemisphere. At the regional level, 3- to 6-month-old infants exhibited leftward asymmetries in functional connectivity strength (FCS) in the temporal cortex, whereas the FCS asymmetries were located in the temporal, frontal, and occipital cortexes for 6- to 9-month-old infants. Furthermore, the 6- to 9-month-old infants also exhibited leftward asymmetries in nodal efficiency around the frontal cortex. These combined findings demonstrate that functional asymmetric organization has emerged in early infancy, which could lay a critical foundation for the development of brain functions (e.g., language and social cognition functions) later in life.