(1) Background: The COVID-19 pandemic is unprecedented and has affected every social class. The prevalence of moderate-to-severe stress and anxiety levels in the general population was reported to be 25%. This study aimed to describe the validation of the Hungarian version of the COVID Stress Scale. (2) Methods: The research study was a cross-section validation study with a representative sample (N = 1200) and a non-representative student sample (N = 350). The translation procedure was a four-step procedure. The interviewers conducted the data collection. (3) Results: The reliability of the Hungarian CSS was assessed using Cronbach’s alpha. Convergent validity was evaluated by correlating the CSS with the PSS and WHO-WBI5. The Cronbach’s alpha coefficient of the CSS-H factors was between 0.844 and 0.907 (representative sample) and between 0.878 and 0.936 (student sample), which qualified as very good. The reliability of the internal consistency was good for all six factors in both samples. The CSS-H total and all-domain scores significantly and positively correlated with the PSS total score and negatively correlated with well-being. (4) Conclusions: The Hungarian COVID Stress Scale is a valid, reliable instrument to measure COVID-19-related distress in the Hungarian population.