The COVID-19 pandemic represents a global health and social challenge. However, the impact of a SARS-CoV-2 infection itself on mental health and sleep quality remains poorly understood. The purpose of the present uncontrolled prospective observational pilot study was to evaluate the impact of past COVID-19 disease on the incidence of quantitative and qualitative sleep disturbances. A group of 61 subjects (37 female, 24 male) reported sleep disturbances that had lasted for at least one month and had started after recovery from COVID-19. The study used self-reported instruments: the Epworth Sleepiness Scale (ESS) and Insomnia Severity Index (ISI), as well as an objective method-actigraphy-for quantitative analysis of sleep architecture. It was shown that sleep disturbances most commonly started after recovery (68.3%, n = 41) and lasted for more than one month (83.6%, n = 51). ESS scores of 7.8 ± 5.0 points indicate moderate daytime sleepiness, and ISI scores of 16.3 ± 5.8 points denote moderate insomnia. ESS scores were negatively correlated with total time in bed (r = -0.3780, = 0.003), total sleep time (r = -0.2969, = 0.020), and wakefulness after sleep onset (r = -0.2654, = 0.039). In addition, ESS scores were correlated negatively with the respondents' age (B = -0.17, = 0.000) and time from COVID-19 onset. A positive correlation was found between wakefulness after sleep onset and ESS scores (B = -0.05, = 0.039). ISI scores were positively correlated with time in bed (r = 0.3275, = 0.010). Female gender was found to be a significant predictor of insomnia's severity (B = 2.159, t = 3.04, = 0.004). In conclusion, patients with a history of COVID-19 report long-lasting sleep disturbances that do not subside spontaneously. In the patient group studied, moderate levels of daytime sleepiness and insomnia were found. The most frequently reported problems included irregular sleep, frequent awakenings, and difficulty maintaining sleep, while normal sleep duration was preserved. These findings underscore the need for continued attention to the long-term consequences of COVID-19 on sleep health and emphasize the importance of targeted interventions to address these enduring sleep disturbances in affected individuals.