Premature birth is associated with high rates of motor and cognitive disability. Investigations have described resting-state functional magnetic resonance imaging (rs-fMRI) correlates of prematurity in older children, but comparable data in the neonatal period remain scarce. We studied 25 term-born control infants within the first week of life and 25 very preterm infants (born at gestational ages ranging from 23 to 29 weeks) without evident structural injury at term equivalent postmenstrual age. Conventional resting-state network (RSN) mapping revealed only modest differences between the term and prematurely born infants, in accordance with previous work. However, clear group differences were observed in quantitative analyses based on correlation and covariance matrices representing the functional MRI time series extracted from 31 regions of interest in 7 RSNs. In addition, the maximum likelihood dimensionality estimates of the group-averaged covariance matrices in the term and preterm infants were 5 and 3, respectively, indicating that prematurity leads to a reduction in the complexity of rs-fMRI covariance structure. These findings highlight the importance of quantitative analyses of rs-fMRI data and suggest a more sensitive method for delineating the effects of preterm birth in infants without evident structural injury.