Background and Objectives: The COVID-19 pandemic brought significant challenges across governmental, industrial, and social systems. Additionally, numerous studies have reported a sharp increase in both mental health issues and musculoskeletal disorders worldwide. This study aimed to investigate whether a specific exercise program could alleviate neck and upper back pain symptoms and improve mood state among healthcare and office employees during the post-COVID-19 period. Materials and Methods: This was an unblinded (open label) randomized controlled trial (both the participants and the researchers knew which treatment or intervention was being administered). In total, 40 healthcare employees from a public hospital and 98 remote office employees, all of whom reported neck and upper back pain, were randomly assigned to an experimental (EG) and control group (CG). The experimental groups underwent the same exercise protocol, while their corresponding control groups underwent the assessments only. Pain assessment using the Visual Analogue Scale (VAS) and mood state using the Feeling Scale (FS) questionnaires of the participants were recorded at baseline (pre-intervention) and immediately following the exercise intervention period of 6 weeks (post-intervention). The intervention consisted of 18 exercise sessions conducted over a 6-week period, with remote office workers participating online and healthcare workers attending exercise sessions on site (at the hospital). Statistical analysis was performed using non-parametric Mann–Whitney and Wilcoxon tests, as appropriate. Results: Following the six-week intervention, the percentage of workers in the EG reporting pain decreased significantly (from 75% to 45% for healthcare workers and from 54% to 25% for office employees), whereas no change was observed for their corresponding control groups. Similarly, the mood state of the EGs significantly improved compared with the control groups, as measured between pre- and post-intervention sessions. Conclusions: The COVID-19 period exacerbated stress and musculoskeletal strain, particularly for workers in demanding occupational roles. To mitigate these effects, exercise programs that can be applied while at work should be implemented, as they are effective in enhancing mood and managing neck pain in employees with physical exertion.