The health crisis triggered by COVID-19 and the preventive measures taken to control it have caused a strong psychological impact on the population, especially on healthcare professionals. Risk exposure, uncertainty about how to approach the disease, care and emotional overburden, lack of resources, or unclear ever-changing protocols are, among others, psychological distress risk factors for the healthcare professionals who have faced this dramatic scenario on the front line. On the other hand, the Sense of Coherence (SOC) is a competence that could help these professionals perceive the situation as understandable, manageable, and meaningful, facilitating the activation of their resilience. This work aims to describe the levels of psychological distress and SOC of healthcare professionals during the crisis caused by COVID-19, the relationship between both variables, and their health status. A cross-sectional descriptive study with a sample of 1459 currently active healthcare workers was developed. GHQ-12 and SOC-13 were used for data collection. Bivariate analyses were performed, including Chi-Squared Test, Student’s T-Test, Analysis of Variance—ANOVA (with Bonferroni test for multiple comparisons), and correlations. Cohen’s d or Cramer’s V effect size measurements were also provided. The results showed that 80.6% of healthcare professionals had psychological distress, and the mean score on the SOC-13 scale was 62.8 points (SD = 12.02). Both psychological distress and SOC were related to the presence of COVID-19 symptoms, as well as with contact history. Professionals with psychological distress showed a lower SOC. Taking care of the mental health of healthcare professionals is essential to effectively cope with the COVID-19 pandemic. Given the psychological impact of working in the current menacing scenario, people on the front line against the disease should be protected, minimizing risks, providing them with resources and support, and fostering their coping skills.