The rapid spread of the coronavirus disease 2019 (COVID-19) has led to high levels of fear worldwide. Given that fear is an important factor in causing psychological distress and facilitating preventive behaviors, assessing the fear of COVID-19 is important. The seven-item Fear of COVID-19 Scale (FCV-19S) is a widely used psychometric instrument to assess this fear. However, the factor structure of the FCV-19S remains unclear according to the current evidence. Therefore, the present study used a network analysis to provide further empirical evidence for the factor structure of FCV-19S. A total of 24,429 participants from Iran (n = 10,843), Bangladesh (n = 9906), and Norway (n = 3680) completed the FCV-19S in their local language. A network analysis (via regularized partial correlation networks) was applied to investigate the seven FCV-19S items. Moreover, relationships between the FCV-19S items were compared across gender (males vs. females), age groups (18–30 years, 31–50 years, and >50 years), and countries (Iran, Bangladesh, and Norway). A two-factor structure pattern was observed (three items concerning physical factors, including clammy hands, insomnia, and heart palpitations; four items concerning psychosocial factors, including being afraid, uncomfortable, afraid of dying, and anxious about COVID-19 news). Moreover, this pattern was found to be the same among men and women, across age groups and countries. The network analysis used in the present study verified the two-factor structure for the FCV-19S. Future studies may consider using the two-factor structure of FCV-19S to assess the fear of COVID-19 during the COVID-19 era.