This article’s main focus is to highlight significant aspects of amino acid solution demineralization. The main part of the amino acid production method requires the provision of downstream treatment solutions for the process of desalination. Electrodialysis (ED) and electrodeionization (EDI) are prospective technologies for such treatment. The article presents a brief review of the first studies and current research on electromembrane desalination of amino acid solutions as well as the analysis of some electrochemical features for the mineral salt–amino acid system (model solution) in an ED process based on the experimental results. The influence of various factors on the desalination of neutral amino acid-containing solutions and on target product losses in this process is estimated. The behavior of aliphatic (alanine) and aromatic (phenylalanine) amino acids in the electromembrane system is considered in mixed solutions with inorganic electrolytes. The influence of various mineral cations (Na+, K+ and NH4+) and anions (NO3−, SO42−, Cl−) on the features of the transport and current−voltage characteristics of ion-exchange membranes in the electrodialysis of phenylalanine- and alanine-containing solutions is considered. A comparative analysis of the desalination parameters of AA solutions in electrodialysis with the following pairs of heterogeneous MA-41/MK-40, MA-40/MK-40 and homogeneous AMT/CMT membranes is carried out. The minimum amount of amino acid loss along with rather high values of the degree of desalination are revealed in electrodialysis with polypropylene spacers in comparison with EDI, ED with a copolymer of styrene and divinylbenzene as spacer, as well as ED with a smooth deionization channel. At the same time, EDI is the most promising method to reach the highest desalination degree in the considered range of mineral salt content.