Radiotherapy employs ionizing radiation to induce lethal DNA lesions in cancer cells while minimizing damage to healthy tissues. Due to their pattern of energy deposition, better therapeutic outcomes can, in theory, be achieved with ions compared to photons. Antiprotons have been proposed to offer a further enhancement due to their annihilation at the end of the path. The work presented here aimed to establish and validate an experimental procedure for the quantification of plasmid and genomic DNA damage resulting from antiproton exposure. Immunocytochemistry was used to assess DNA damage in directly and indirectly exposed human fibroblasts irradiated in both plateau and Bragg peak regions of a 126 MeV antiproton beam at CERN. Cells were stained post irradiation with an anti-γ-H2AX antibody. Quantification of the γ-H2AX foci-dose relationship is consistent with a linear increase in the Bragg peak region. A qualitative analysis of the foci detected in the Bragg peak and plateau region indicates significant differences highlighting the different severity of DNA lesions produced along the particle path. Irradiation of desalted plasmid DNA with 5 Gy antiprotons at the Bragg peak resulted in a significant portion of linear plasmid in the resultant solution.