Poly(acrylic acid)-poly(vinyl amine) block copolymer nanogels were produced for the first time by a simple and environmentally friendly irradiation method. To enhance biocompatibility and achieve tumor-specific targeting, the nanogels underwent modifications by incorporating bovine serum albumin and folic acid. Subsequently, methotrexate (MTX) was loaded into the modified nanogels and in vitro MTX release profile from nanogels was studied at different pH values. The amount of MTX released from the nanogels was approximately 3.3 times higher at pH 3.0 compared to pH 7.4, indicating the relative stability of the nanoparticles in blood during in vivo circulation, and their rapid release after being internalized in the acidic environment once they enter the tumor. The cytotoxicity of the nanogels, particularly the MTX loaded nanogels, was evaluated using an MTT assay on both L929 fibroblast and MCF-7 breast cancer cell lines. The results indicated that the nanogels demonstrated notably higher cytotoxic effects on the cancer cells compared to the healthy cells. In conclusion, methotrexate-functionalized nanogels showed improved and selective cytotoxic activity against human breast cancer cells, providing great motivation to continue evaluating the therapeutic benefits of these formulations for further in vivo preclinical testing.