The climate crisis, growing pollution of the environment with waste, and ubiquitous microplastics have encouraged the search for new methods and new opportunities to use natural materials in the least harmful processes. Replacing synthetic materials with raw materials is not only a matter of “fashion”, but also a necessity. Therefore, this study aimed to produce fibers from an aqueous solution containing the highest possible concentration of soy protein isolate (SPI) through solution-blowing. As the aqueous solution of SPI has no fiber-forming potential, polyethylene oxide (PEO) was used as the carrier/matrix. The rheology of the aqueous PEO solution and PEO/SPI blends (flow curves, loss modulus, and storage modulus) was then analyzed. The proportions of the PEO/SPI mixtures and the process parameters were determined on this basis. As a result of the conducted research, nanofibers were produced from water solutions of PEO/SPI with a soy protein content of up to 7.88%, with a PEO share of 1.25%. The average diameter of the obtained fibers was 225−495 nm, depending on the process parameters and SPI content—as the SPI content in the PEO/SPI mixture increased, the average fiber diameter decreased. The production of nanofibers with a high soy protein content increases their application possibilities. Firstly, due to a much larger surface area, and secondly, due to the presence of numerous functional groups in the protein structure, which can be a place of attachment for additional compounds that give the obtained nanofibers the desired properties.