Our opinions and views of life can be shaped by how we perceive the opinions of others on social media like Facebook. This dependence has increased during COVID-19 periods when we have fewer means to connect with others. However, fake news related to COVID-19 has become a significant problem on Facebook. Bengali is the seventh most spoken language worldwide, yet we are aware of no previous research that studied the prevalence of COVID-19 related fake news in Bengali on Facebook. In this paper, we develop machine learning models to detect fake news in Bengali automatically. The best performing model is BERT, with an F1-score of 0.97. We apply BERT on all Facebook Bengali posts related to COVID-19. We find 10 topics in the COVID-19 Bengali fake news grouped into three categories: System (e.g., medical system), belief (e.g., religious rituals), and social (e.g., scientific awareness).