Unlike its short-term impact on consumption and income, forced migration is expected to deliver a permanent shock to the overall well-being of households, specifically children in the stage of infancy. Studies on the effect of forced migration on child cognitive well-being are few in number. Therefore, the present study is intended to examine the consequences of forced migration during infancy on child cognition at later age. We hypothesized that the effect of forced migration on child cognitive well-being can be mitigated by social support. The study used longitudinal data from three waves of the Young Lives Study (YLS) conducted in 2002, 2006–2007, and 2009 in the state of Andhra Pradesh, India. We used bivariate and multivariate regression models to analyze the consequences of forced migration in early childhood on the cognitive well-being in later childhood. The information on forced migration was collected in Wave 1 (at age 1), whereas the information on the cognitive well-being of the children was collected in Wave 3 (at age 8). Child cognitive well-being was measured using scores obtained by the children on the Peabody Picture Vocabulary Test (PPVT), math, Early Grade Reading Assessment (EGRA), and memory tests. The results of the bivariate analysis show that the mean PPVT, math, EGRA, and memory scores obtained by children from the migrated households were lower than those obtained by children from the non-migrated households. Results of the multivariate linear regression models also show that children from the migrated households were statistically less likely to achieve higher scores on math (coefficient: -2.008, 95% C.I.-3.108, -0.908), EGRA (coefficient: -0.746, 95% C.I.-1.366, -0.126), and memory (coefficient: -0.503, 95% C.I. -0.834, -0.173) as compared to children from the non-migrated households. Our findings also indicate that the effect of forced migration on child cognitive well-being was not mitigated by social support. Findings of this study conclude that forced migration during infancy has a significant effect on child cognitive well-being at later age. Therefore, interventions should be made, paying attention to the most vulnerable children who were displaced during critical development ages.