During the pandemic, health and environmental issues were re-evaluated, stimulating interest in organic food. Organic milk is more beneficial than conventional milk in terms of the health-promoting substances (e.g., vitamins, fatty acids), particularly regarding its protein and lipid fractions. Poland is the main producer of cow’s milk in the EU, but only 0.2% of this production is organic. To identify the antecedents and obstacles to increasing organic milk production in Poland, the aim of this study is to explore the low level of organic cow’s milk output in Poland compared with sector leaders in the EU. We analyzed statistics on milk production, including unpublished data collected by the Agricultural and Food Quality Inspection, Poland, with the use of descriptive statistics and frequency distributions. Over the period 2010–2020, the number of farms producing and selling organic milk and the number of farms with organic pastures and meadows decreased significantly in Poland. A limited number of certified farms sell their milk as organic. If all production of organic milk was sold as organic, the supply would have increased by 56% in 2020. Organic milk processing is highly concentrated which is an obstacle to the development of organic milk farming. Due to its high instability and the spatial differences in the locations of sellers (producers) and buyers (processors) and inconsistent production volumes, the supply of organic cow’s raw milk does not meet the demand from Polish dairies. Cooperation between producers and processors is essential. Providing organic dairy farms with production and market advice, as well as technical support, is crucial for the development of farms and the organic milk sector as a whole, as is, to a certain extent, evidenced by Austria. The specific nature of the raw milk market requires the procurement of organic milk on a lasting basis regarding guarantees of purchase and farmgate prices. In this way, the continuity of organic raw milk supply would be secured and the sector of organic dairy products should grow.