Matrix metalloproteinases (MMPs) are extracellular matrix degradation factors, promoting cancer progression. Hence, they could provide an enzyme-assisted delivery of doxorubicin (DOX) in cancer treatment. In the current study, the intercalation process of DOX and tetrapeptide–DOX, the product of the MMPs’ cleavage of carrier-linked DOX, into dsDNA was investigated using stationary and time-resolved fluorescence spectroscopy, UV-Vis spectrophotometry and isothermal titration calorimetry (ITC). The molecular dynamics (MD) simulations on the same tetrapeptide–DOX…DNA and DOX…DNA systems were also performed. The undertaken studies indicate that DOX and tetrapeptide–DOX can effectively bond with dsDNA through the intercalation mode; however, tetrapeptide–DOX forms less stable complexes than free DOX. Moreover, the obtained results demonstrate that the differences in DNA affinity of both forms of DOX can be attributed to different intercalation modes. Tetrapeptide–DOX shows a preference to intercalate into DNA through the major groove, whereas DOX does it through the minor one. In summary, we can conclude that the tetrapeptide–DOX intercalation to DNA is significant and that even the lack of non-specific proteases releasing DOX from the tetrapeptide conjugate, the presence of which is suggested by the literature for the efficient release of DOX, should not prevent the cytostatic action of the anthracycline.