Background: To date, evidence about sleep disturbances among post-COVID-19 patients is limited. This study aimed to evaluate sleep quality after hospitalization due to SARS-CoV-2 infection. Methods: In-person follow-up was conducted in patients with prior hospitalization due to COVID-19 1(Τ1), 3(Τ2), and 6 (Τ3) months after hospital discharge. Patients were asked to complete questionnaires concerning sleep quality: the Pittsburgh Sleep Quality Index (PSQI), the Epworth Sleepiness Scale (ESS), the Athens Insomnia Scale (AIS), the Fatigue Severity Scale (FSS), and the Stop-BANG (S-B) questionnaire. Results: In total, 133 patients were enrolled (mean age: 56.0 ± 11.48 years, 59.4% males). The most frequently reported comorbidity was arterial hypertension (29.8% of patients), while 37.4% of patients had no comorbidities. The majority of participants exhibited poor sleep quality (global PSQI ≥ 5) at T1 (84.3%), T2 (75.7%), and T3 (77.4%). Insomnia was observed in 56.5%, 53.5%, and 39.2% of participants, respectively (AIS ≥ 6). An FSS score ≥ 4 was observed in 51.2%, 33.7%, and 29.1% of participants at T1, T2, T3, respectively. Elapsed time was found to be negatively and independently associated with the global PSQI, PSQI C5-Sleep disturbance, PSQI C7-Daytime dysfunctions, FSS, and AIS after adjustment for possible confounders. No significant difference was found between groups with good and poor sleep quality (based on the global PSQI) with respect to gender (p = 0.110), age (p = 0.528), BMI (p = 0.816), smoking status (p = 0.489), hypertension (p = 0.427), severity of disease (p = 0.224), the Charlson Comorbidity Index (p = 0.827), or the length of hospital stay (p = 0.162). Participants with excessive daytime sleepiness (EDS) and patients with severe fatigue (FSS ≥ 4) were significantly younger. Females presented a higher rate of insomnia symptoms (55.7% vs. 44.3%, p < 0.001). Conclusions: Several sleep disturbances were observed after hospital discharge for COVID-19 pneumonia at certain time points; However, the improvement over time was remarkable in most domains of the assessed questionnaires.