While the coronavirus disease 2019 (COVID-19) pandemic wreaked havoc across the globe, we have witnessed substantial mis- and disinformation regarding various aspects of the disease. We conducted a cross-sectional study using a self-administered questionnaire for the general public (recruited via social media) and healthcare workers (recruited via email) from the State of Qatar, and the Middle East and North Africa region to understand the knowledge of and anxiety levels around COVID-19 (April–June 2020) during the early stage of the pandemic. The final dataset used for the analysis comprised of 1658 questionnaires (53.0% of 3129 received questionnaires; 1337 [80.6%] from the general public survey and 321 [19.4%] from the healthcare survey). Knowledge about COVID-19 was significantly different across the two survey populations, with a much higher proportion of healthcare workers possessing better COVID-19 knowledge than the general public (62.9% vs. 30.0%, p < 0.0001). A reverse effect was observed for anxiety, with a higher proportion of very anxious (or really frightened) respondents among the general public compared to healthcare workers (27.5% vs. 11.5%, p < 0.0001). A higher proportion of the general public tended to overestimate their chance of dying if they become ill with COVID-19, with 251 (18.7%) reporting the chance of dying (once COVID-19 positive) to be ≥25% versus 19 (5.9%) of healthcare workers (p < 0.0001). Good knowledge about COVID-19 was associated with low levels of anxiety. Panic and unfounded anxiety, as well as casual and carefree attitudes, can propel risk taking and mistake-making, thereby increasing vulnerability. It is important that governments, public health agencies, healthcare workers, and civil society organizations keep themselves updated regarding scientific developments and that they relay messages to the community in an honest, transparent, unbiased, and timely manner.