This study explored the perceived change in tobacco use during the COVID-19 pandemic and its associated factors among older adults residing in Rohingya refugee camps, also referred to as Forcibly Displaced Myanmar Nationals in Bangladesh. The study followed a cross-sectional design and was conducted in October 2020 among 416 older adults aged 60 years and above. A purposive sampling technique was applied to identify eligible participants, and face-to-face interviews were conducted using a pre-tested semi-structured questionnaire to collect the data. Participants were asked if they noted any change in their tobacco use patterns (smoking or smokeless tobacco) during the COVID-19 pandemic compared to pre-pandemic. Binary logistic regression models determined the factors associated with the perceived change in tobacco use. More than one in five participants (22.4%) were current tobacco users, of whom 40.8% reported a perceived increase in tobacco use during the COVID-19 pandemic. Adjusted analysis revealed that participants who were concerned about COVID-19 had significantly (p < 0.05) lower odds of perceived increase in tobacco use (aOR = 0.22, 95% CI: 0.06-0.73), while older adults who were overwhelmed by COVID-19 (aOR = 0.26, 95% CI: 0.06-1.18) and communicated less frequently with others during the pandemic than before (aOR = 0.19, 95% CI: 0.03-1.20) had marginally significantly (p < 0.1) lower odds of perceived increase in tobacco use during this pandemic. Relevant stakeholders, policymakers, and practitioners need to focus on strengthening awareness-raising initiatives as part of an emergency preparedness plan to control tobacco use during such a crisis period.