Background Pandemics such as the current COVID-19 pandemic are often associated with heightened fear and significant adjustments in health behaviours. Aim This study aimed to assess perceived risk, anxiety and protective behaviours of the general public during the early phase of the coronavirus disease (COVID-19) pandemic in Nigeria. Methods An online cross-sectional study among 1197 respondents aged 18 years and above between 27 April to 16 May 2020. Result More than half (61.9%) of the respondents had high risk perception towards COVID-19, and high anxiety level was found in 37.2%. Male gender, being a Christian, having more than 12 years of formal education and high risk perception were positively associated with observance of more than one protective measure against COVID-19. The predictors of COVID-19-related anxiety were high risk perception and being a Muslim. Conclusions This study showed that risk perception has an influence on both anxiety and observance of protective behaviours. Being a novel experience, this research has implications to support current and future responses to a pandemic experience.