The emergence of plant-based milk alternatives or milk analogs seems to provide a sustainable solution to feeding the growing human population and continues to gain momentum across the globe. However, despite the advantages of plant-based milk analogs, several studies have linked consumption of these plant-based derivatives with other negative effects, such as allergic reactions, toxic chemical components, and susceptibility to microbial contamination, in addition to improper nutritional balance. Therefore, the potential use of novel ingredients in the formulation of plant-based milk analogs makes it important to consider food safety concerns that these ingredients might introduce. The food safety concerns pertaining to plant-based food production and processing include the presence of allergens (from ingredients like soy, gluten, and nuts), anti-nutritional factors (such as saponins, alkaloids, and isoflavones), mycotoxins, potential contamination with pathogenic microorganisms (e.g., Salmonella spp., E. coli, Bacillus spp., Listeria spp., Clostridium sporogenes, and Geobacillus stearothermophilus), pesticide residues, toxic metal elements, and process-induced toxins (e.g., polycyclic aromatic hydrocarbons, heterocyclic aromatic amines, and nitrosamines), among others. Concerted research efforts are required for thorough risk assessment of plant-based milk analogs to ensure wider successful adoption and use of newer products, which are palatable as well as safe and nutritionally adequate. In addition to the food safety risks associated with plant-based milk analogs, a dilemma in the introduction of these innovative products is their naming and regulatory standards. Since national legislation on food standards and labeling varies from country to country, principle terminology in categorizing these plant-based milk analogs has been under debate at the international level. Current regulations provide standards for traditional dairy products but lack the same regulations for similar plant-based products. Globally, plant-based milk analogs will continue to be a major research area for regulatory bodies in the newer product development category.