Among various health implications for an older adult, cognitive impairment and related dementias are significant public health concerns and lack due attention in the in-policy arena. Therefore, the present study explores the prevalence and determinants of cognitive impairment among older adults in India with special reference to the migrant status of older adults. The study utilizes cross-sectional data obtained from the recent release of the Longitudinal Ageing Study in India (LASI) wave 1 (2017–18). The study used univariate, bivariate, and multivariate analyses to describe the prevalence of cognitive impairment among the older adults aged 60 and above by migration and gender status. We then determined the association between cognitive impairment with migration status, individual factors, health conditions, and socioeconomic conditions. Overall, the prevalence of cognitive impairment among migrant and non-migrant older adults was 16.0% and 9.5%, respectively. The prevalence of cognitive impairment was found to be varied with socioeconomic, demographic, and health conditions of older adults. In an unadjusted scenario, older migrant adults were 1.57 times more likely to develop cognitive impairment [UOR; 1.57, CI: 1.45–1.70] which was 1.14 times after adjusting for covariates [AOR; 1.14, CI: 1.03–1.26]. Migrant female older adults [AOR:2.28, CI: 2.02–2.59], migrant male older adults [AOR:1.29, CI: 1.08–1.53], and non-migrant female older adults [AOR:2.12, CI: 1.86–2.46] were at high risk of cognitive impairment compared to non-migrant male older adults. The prevalence and the risk of cognitive impairment were strongly associated with the migration status of older adults in India. Migrant older adults especially female migrants under different socioeconomic, demographic, and health conditions were at high risk of cognitive impairment.