Purpose Few studies have addressed the sleep disturbances of healthcare workers during crisis events of public health. This study aimed to examine the sleep quality of frontline healthcare workers (FLHCW) in Bahrain during the COVID-19 pandemic, and compare it with the sleep quality of non-frontline healthcare workers (NFLHCW). Methods Healthcare workers (n = 280) from multiple facilities belonging to the Ministry of Health, Bahrain, were invited to participate in this cross-sectional study. An online questionnaire, including socio-demographics, the Pittsburgh Sleep Quality Index (PSQI), and the Perceived Stress Scale (PSS), was used to evaluate sleep disturbances and stress levels of healthcare workers. Poor sleep quality was defined as PSQI ≥ 5 and moderate-severe stress as PSS ≥ 14. Descriptive statistics were used to compare the scores of FLHCW and NFLHCW. Univariate and multivariate binary logistic regressions were used to identify predictors of poor sleep quality, moderate-severe stress, and the combined problem of poor sleep quality and moderate-severe stress. Results A total of 257 participants (129 FLHCW and 128 NFLHCW) provided usable responses. The overall PSQI and PSS scores were 7.0 ± 3.3 and 20.2 ± 7.1, respectively. The FLHCW scored higher in the PSQI and PSS compared with the NFLHCW; however, the differences in the PSQI and PSS scores were not statistically significant. For the FLHCW, 75% were poor sleepers, 85% had moderate-severe stress, and 61% had both poor sleep quality and moderate-severe stress. For the NFLHCW, 76% were poor sleepers, 84% had moderate-severe stress, and 62% had both poor sleep quality and moderate-severe stress. Female sex and professional background were the predictors of poor sleep quality and stress. Conclusions Poor sleep quality and stress are common during the COVID-19 crisis. Approximately, 60% of both FLHCW and NFLHCW have poor sleep quality combined with moderate-severe stress.