The COVID-19 crisis disrupted the economic life of the entire world and caused various disturbances at different levels in economies and societies. Consequently, the study of the economic impact of the health crisis became necessary to identify the influences that the health crisis had on numerous activities, including economic ones. There are calls for more studies to be conducted about the effects of COVID-19 at different levels so that lessons can be learned. The present paper answers these calls and focuses on the analysis of the impact of the COVID-19 crisis on international trade at the country level by investigating two European countries, Romania and Poland. First, it analyzes the macro-level context of the two countries during the COVID-19 pandemic. Then, a regression methodology is employed to measure the impact of the COVID-19 burden (which includes the number of cases and the number of deaths related to COVID-19) on the export and import flows in Romania and Poland. The investigation refers to the first two years of the COVID-19 pandemic, 2020–2021, which were the most significant. The results of the regression analysis showed that international trade was affected by the COVID-19 burden in the two countries, but the influences were different in the two countries. Exports and imports in Poland were more affected by COVID-19 than exports and imports in Romania. COVID-19 also had a higher impact on the import than the export flows in both countries during the period considered. The negative assumed relationships between COVID-19 burden and international trade flows were not verified in these specific country cases. This paper provides more evidence about the economic impact of the COVID-19 crisis, contributing to a better understanding of the economic effects of health crises in general.