Older adults residing in refugee settlements with unhealthy living environments, inadequate access to health care services, and limited psychosocial support are vulnerable to experience mental health problems jeopardizing their mental well-being. The present study aims to explore the mental well-being status and its socio-economic determinants among the older adults living in the Rohingya refugee camp in Bangladesh. This cross-sectional study was conducted among adults aged ≥ 60 residing in five sub-camps within the Rohingya refugee camp of Cox’s Bazar, Bangladesh. Data were collected through face-to-face interviews conducted between November and December 2021. The 14-item Warwick-Edinburgh Mental Well-being Scale was used to assess mental well-being. A cumulated score was derived using the scale ranging from 14 to 70, with higher scores indicating greater levels of mental well-being. A generalized linear regression model was used to examine the socio-economic factors associated with the mental well-being of older adults. A total of 864 older adults participated in the study having a mean mental well-being score of 45.4. Regression analysis revealed that the difference in the logs of mental well-being score was expected to be significantly lower among participants aged 70–79 years (β: − 1.661; 95% CI: − 2.750 to − 0.572; p = 0.003), aged ≥ 80 years (β: − 3.198; 95% CI: − 5.114 to − 1.282; p = 0.001), and those with any non-communicable chronic conditions (β: − 2.903; 95% CI: − 3.833 to − 1.974; p < 0.001) when compared to their counterparts. Conversely, the difference in the logs of mental well-being score was expected to be significantly higher among individuals with formal schooling (β: 3.370, 95% CI: 1.855 to 4.886, p < 0.001) and those having additional income besides aid (β: 1.629; 95% CI: 0.642 to 2.615; p = 0.001), compared to their respective counterparts. Our findings highlight the need to provide psychosocial assistance to older individuals, particularly those who live in large families, suffer from chronic diseases, and live in socio-economic deprivation.