Enzyme purification is a lengthy, expensive, and demanding process that usually results in low yield and loss of enzyme activity. Extraction procedures are among the most widely used methods for purifying various molecules. However, the use of conventional solvents, such as organic solvents, leads to denaturation of enzymes. The use of aqueous two-phase systems (ATPS) to purify biomolecules has been shown to be an effective and environmentally friendly method. Among the various ATPS, ATPS based on deep eutectic solvents (DES) are attracting special attention due to their low toxicity, high biodegradability, and cost-effectiveness. In recent years, attention has also focused on the use of microextractors for biomolecule purification because they intensify the process and are less likely to disrupt the structure of biomolecules. In this work, an integrated system of microextractor and microseparator connected in series was developed for continuous microextraction of proteins, i.e., extraction of the enzyme laccase from Trametes versicolor, using an ATPS based on DES. A total of 15 DESs were synthesized and characterized. In a series of batch extractions, the influence of DES composition and salt concentration (K2HPO4) on the efficiency of laccase enzyme extraction was investigated. The system consisting of the eutectic solvent choline-chloride:propylene glycol:zinc dichloride 1:4:0.02 (ChCl:PG:ZnCl2 1:4:0.02) and an aqueous solution of K2HPO4 with a concentration of γ = 0.5 g/mL proved to be the most efficient system for laccase enzyme extraction. In the next step, the influence of enzyme concentration on extraction efficiency was tested using the selected system. The obtained results showed that increasing the enzyme concentration positively affected the extraction efficiency. To intensify the process, the extraction was performed in a microextractor, and the influence of the channel diameter and residence time on the extraction efficiency was studied. The highest efficiency of enzyme extraction in the microextractor (d = 500 μm) was E = 88.34 ± 1.04 % and it was achieved at a residence time of τ = 12 s. The extraction process in the microextractor was successfully described by a 2D mathematical model. After optimization of the extraction process, the microextractor was connected in series with a microseparator, in which the extract and raffinate phases were successfully separated. At the very end, the developed method was tested on the crude laccase enzyme produced by the fermentation of Trametes versicolor, and the extracted enzyme was used to remove the aniline-based textile dye.