Epigenetic age acceleration (AA) has been associated with adverse environmental exposures and many chronic conditions. We estimated, in the NINFEA birth cohort, infant saliva epigenetic age, and investigated whether parental socio-economic position (SEP) and pregnancy outcomes are associated with infant epigenetic AA. A total of 139 saliva samples collected at on average 10.8 (range 7–17) months were used to estimate Horvath’s DNA methylation age. Epigenetic AA was defined as the residual from a linear regression of epigenetic age on chronological age. Linear regression models were used to test the associations of parental SEP and pregnancy outcomes with saliva epigenetic AA. A moderate positive association was found between DNA methylation age and chronological age, with the median absolute difference of 6.8 months (standard deviation [SD] 3.9). The evidence of the association between the indicators of low SEP and epigenetic AA was weak; infants born to unemployed mothers or with low education had on average 1 month higher epigenetic age than infants of mothers with high education and employment (coefficient 0.78 months, 95% confidence intervals [CIs]: −0.79 to 2.34 for low/medium education; 0.96, 95% CI: −1.81 to 3.73 for unemployment). There was no evidence for association of gestational age, birthweight or caesarean section with infant epigenetic AA. Using the Horvath’s method, DNA methylation age can be fairly accurately predicted from saliva samples already in the first months of life. This study did not reveal clear associations between either pregnancy outcomes or parental socio-economic characteristics and infant saliva epigenetic AA.