To meet the requirements of novel therapies, effective treatments should be supported by diagnostic tools characterized by appropriate analytical and working parameters. These are, in particular, fast and reliable responses that are proportional to analyte concentration, with low detection limits, high selectivity, cost-efficient construction, and portability, allowing for the development of point-of-care devices. Biosensors using nucleic acids as receptors has turned out to be an effective approach for meeting the abovementioned requirements. Careful design of the receptor layers will allow them to obtain DNA biosensors that are dedicated to almost any analyte, including ions, low and high molecular weight compounds, nucleic acids, proteins, and even whole cells. The impulse for the application of carbon nanomaterials in electrochemical DNA biosensors is rooted in the possibility to further influence their analytical parameters and adjust them to the chosen analysis. Such nanomaterials enable the lowering of the detection limit, the extension of the biosensor linear response, or the increase in selectivity. This is possible thanks to their high conductivity, large surface-to-area ratio, ease of chemical modification, and introduction of other nanomaterials, such as nanoparticles, into the carbon structures. This review discusses the recent advances on the design and application of carbon nanomaterials in electrochemical DNA biosensors that are dedicated especially to modern medical diagnostics.