Vaccine hesitancy is widespread in many parts of the globe, particularly in low–middle-income countries. Therefore, we surveyed a sample of hospitalized COVID-19 patients to assess COVID-19 vaccine acceptance and vaccine hesitancy in a low–middle-income country. A cross-sectional sample of 385 confirmed reverse transcriptase–polymerase chain reaction COVID-19 patients treated at secondary and tertiary care hospitals in Punjab, Pakistan, were analyzed to assess COVID-19 vaccine uptake and vaccine hesitancy. The construct validity and reliability of the 11-item vaccine hesitancy questionnaire were also examined. In addition, multivariate logistic regression was used. The majority of the COVID-19 patients admitted to hospitals were not vaccinated (84%). Of those who were willing to receive vaccination, the majority (55%) considered vaccines an effective way to protect people from COVID-19. However, those who were not willing to receive their COVID-19 vaccine had significantly higher hesitancy than those willing to receive their COVID-19 vaccine. In addition, older hospitalized COVID-19 patients aged 60 years or above (20–29 years: OR 0.10; 95% CI 0.01–0.72, p = 0.001) and patients from urban areas (OR 3.16 95% CI 1.27–7.87, p = 0.013) were more likely to receive the COVID-19 vaccine than younger patients and patients from rural areas. Patients with no formal education had significantly higher hesitancy (OR 5.26; 96% CI 1.85–14.97, p = 0.002) than participants with graduation and above education. More than half of the study’s participants did not trust information shared on social media about COVID-19 vaccines and cited newspapers/news channels as their main source of information. The study provides important insights into COVID-19 vaccine acceptance and the impact of vaccination campaigns. Many unvaccinated COVID-19 patients in hospitals highlight the need for an effective vaccination drive to protect people from acquiring infection and subsequent hospitalization.