Increasing longevity, along with an aging population in Europe, has caused serious concerns about diet-related chronic diseases such as obesity, diabetes, cardiovascular diseases, and certain cancers. As recently noted during the coronavirus pandemic, regular exercise and a robust immune system complemented by adequate consumption of fruit and vegetables are recommended due to their known health benefits. Although the volume of fresh vegetable consumption in the EU is barely growing, demand for diversified, nutritious, and exotic vegetables has been increasing. Therefore, the European market for fresh Asian vegetables is expected to expand across the EU member states, and the introduction of new vegetables has enormous potential. We conducted this review to address the high number and wide range of Asian vegetable species with a commercial potential for introduction into the current European vegetable market. Many of them have not received any attention yet. Four Asian vegetables: (1) Korean ginseng sprout, (2) Korean cabbage, (3) Coastal hog fennel and (4) Japanese (Chinese or Korean) angelica tree, are further discussed. All of these vegetables possess several health benefits, are increasingly in demand, are easy to cultivate, and align with current trends of the European vegetable market, e.g., vegetables having a unique taste, higher value, are decorative and small. Introducing Asian vegetables will enhance the diversity of nutritious horticultural products in Europe, associated with all their respective consumption benefits. Future research on the Asian vegetable market within Europe is needed. In addition, experimental studies of Asian vegetables under practical conditions for their production in different European environments are required. Economic, social, and ecological aspects also ought to be considered.