The current cross-sectional study was conducted among 864 older adults aged ≥ 60 years residing in Rohingya refugee camp through face-to-face interviews during November–December 2021. COVID-19-related anxiety was measured using the five-point Coronavirus Anxiety Scale (CAS) and perceived stress using the 10-point Perceived Stress Scale (PSS). The linear regression model identified the factors associated with COVID-19-related anxiety and perceived stress. The prevalence of COVID-19-related anxiety and perceived stress was 68% and 93%, respectively. The average COVID-19-related anxiety score expected to be significantly higher among those who were physically inactive, concerned about COVID-19, had a close friend/family member diagnosed with COVID-19, and had some difficulty in getting food and routine medical care during the COVID-19 pandemic. Meanwhile, the average perceived stress score was expected to be significantly higher among those without partners, who were feeling overwhelmed by COVID-19, and who experienced COVID-19-related anxiety during the pandemic. The findings suggest providing immediate psychosocial support to older Rohingya adults.