Adopting a cross-sectional study design, we aimed to examine the prevalence of psychological problems in different healthcare workers during the COVID-19 pandemic in the hospitals in these COVID-19 hotspots (Da Nang city and Quang Nam province) and to explore the socioeconomic and COVID-19 control-related factors that are associated with various psychological problems. A total of 611 healthcare workers were included in the final analysis from 1 August 2020 to 31 August 2020. The prevalence of anxiety, depression, insomnia, and overall psychological problems was 26.84%, 34.70%, 34.53%, and 46.48%, respectively. The prevalence rates of anxiety were approximately equal amongst the groups of healthcare workers, and moderate-to-severe anxiety was the most common in physicians (11.11%). The prevalence of depression was the highest in nurses (38.65%) and moderate-to-severe depression was mainly found in physicians (11.81%). The prevalence rates of insomnia were 34.03% in physicians, 36.20% in nurses, and 31.21% in technicians; in particular, the rate of moderate-to-severe insomnia was higher in physicians and nurses compared to technicians. The prevalence of overall moderate-to-severe psychological problems was the highest among physicians (14.58%), followed by nurses (12.58%) and technicians (9.22%). Statistically significant associated factors of current psychological problems were the occupations of physicians or nurses, less than 1 year of experience, university education, living with 4–5 people, reporting 1000–5000 m distance between home and workplace, participating in the COVID-19 control for less than 1 week, being under social isolation at home, being affected a lot by the community, reporting inadequate equipment in current workplace conditions, frequently working in the department directly in contact with the COVID-19 patients, and feeling anxious, stressed, or sad about current works. Present findings can provide valuable evidence for the policymakers and managers to adopt supportive, encouraging, motivational, protective, training, and educational interventions into healthcare workforce in other parts of Vietnam.