Objectives: Burnout syndrome is expected among healthcare workers facing extended periods of physical and psychological stress. Physical and psychosocial factors affect the aetiology of healthcare workers' musculoskeletal pain. This study aimed to determine healthcare workers' burnout syndrome levels at a hospital during the COVID-19 pandemic, investigating burnout syndrome's relationship with lower back pain, neck pain, depression and anxiety. Methods: This prospective observational study employed a Google Forms questionnaire, and 120 training and research hospital employees volunteered to participate. The questionnaire included the Maslach Burnout Inventory, Pain-Visual Analog Scale, Neck Disability Index, Oswestry Disability Questionnaire and Hospital Anxiety and Depression Scale. Results: Fifty-four participants (45%) had moderate emotional exhaustion, and 20 (16%) had severe emotional exhaustion. Eighty-two (68%) had mild depersonalisation and 38 (32%) had moderate depersonalisation, and 120 (100%) had severe reduced personal accomplishment. Moreover, 68.3% of volunteers complained of neck pain over the last year, while 51.7% complained of lower back pain. Relationships were observed between: emotional exhaustion, lower back pain, neck pain, lower back disability, neck disability, anxiety scores and depression scores; depersonalisation, neck pain, anxiety scores and depression scores; and personal accomplishment, neck pain, neck disability, back disability, anxiety scores and depression scores. Lower back disability was significantly higher among participants not infected with the SARS-CoV-2. Anxiety was significantly higher among participants infected with the SARS-CoV-2. Conclusions: Burnout is a risk factor for musculoskeletal pain among healthcare workers. Therefore, healthcare workers require physical and psychological support during crises such as pandemics.