Damaged DNA bases are removed by the base excision repair (BER) mechanism. This enzymatic process begins with the action of one of DNA glycosylases, which recognize damaged DNA bases and remove them by hydrolyzing N-glycosidic bonds with the formation of apurinic/apyrimidinic (AP) sites. Apurinic/apyrimidinic endonuclease 1 (APE1) hydrolyzes the phosphodiester bond on the 5′-side of the AP site with generation of the single-strand DNA break. A decrease in the functional activity of BER enzymes is associated with the increased risk of cardiovascular, neurodegenerative, and oncological diseases. In this work, we developed a fluorescence method for measuring the activity of key human DNA glycosylases and AP endonuclease in cell extracts. The efficacy of fluorescent DNA probes was tested using purified enzymes; the most efficient probes were tested in the enzymatic activity assays in the extracts of A549, MCF7, HeLa, WT-7, HEK293T, and HKC8 cells. The activity of enzymes responsible for the repair of AP sites and removal of uracil and 5,6-dihydrouracil residues was higher in cancer cell lines as compared to the normal HKC8 human kidney cell line.