Stress inherent to health care, which is characterized by work overload and shortage of specialized staff, is associated with decreased quality of life and suboptimal patient care. Mindfulness-based programs have proved to be effective in reducing stress in healthcare providers. This study aims to assess the feasibility of an 8-week mindfulness program to reduce the burnout levels of the staff of a pain clinic in a tertiary public hospital. A longitudinal study with a within subject pre/post-intervention design, consisting of daily face-to-face 10-min sessions and the creation of a virtual group using a social media platform. Variables measured: burnout, mindfulness, empathy, self-compassion, and demographic characteristics. Program feasibility (i.e., reach, adherence, acceptability, and preliminary effectiveness) was evaluated in 10 participants (6 physicians, 2 nurse practitioners, 1 nursing assistant, and 1 administrative). The results revealed a high reach (i.e., participation rate of 90%), excellent adherence to the program (daily practice 95% of times), and very good acceptability of the group format and satisfaction with most treatment components. Regarding potential effectiveness, we report the results of the Wilcoxon signed-rank tests and its associated effect size (r). We observed improvements in mindfulness and all its subscales (−2.077 ≤ Z ≤ −2.703, 0.69 ≤ r ≤ 0.90, all p < 0.05) except for non-reactivity and all subcomponents of self-compassion (−2.501 ≤ Z ≤ −2.611, 0.83 ≤ r ≤ 0.87, all p < 0.05) but not on its global self-compassion score. Empathy and burnout did not change. In an exploratory manner, however, we found significant reductions in the burnout component of emotional exhaustion, but only in physicians (Z = −2.201, p = 0.028, r = 0.73). We believe that the 8-week mindfulness-based program described in the present investigation might be a feasible and potentially effective method that can be easily implemented to reduce burnout and promote mindfulness in specialized pain clinics