We investigated the potential of the energy resolving hybrid pixel detector Timepix contacted to a CdTe sensor layer for the search for the neutrinoless double-beta decay of Cd-116. We found that a CdTe sensor layer with 3 mm thickness and 165 mu m pixel pitch is optimal with respect to the effective Majorana neutrino mass (m(beta beta)) sensitivity. In simulations, we were able to demonstrate a possible reduction of the background level caused by single electrons by approximately 75% at a specific background rate of 10(-3) counts/(kg x keV x yr) at a detection efficiency reduction of about 23% with track analysis employing random decision forests. Exploitation of the imaging properties with track analysis leads to an improvement in sensitivity to m(beta beta) by about 22%. After 5 years of measuring time, the sensitivity to m(beta beta) of a 420 kg CdTe experiment (90% Cd-116 enrichment) would be 59 meV on a 90% confidence level for a specific single-electron background rate of 10(-3) counts/(kg x keV x yr). The alpha-particle background can be suppressed by at least about six orders of magnitude. The benefit of the hybrid pixel detector technology might be increased significantly if drift-time difference measurements would allow reconstruction of tracks in three dimensions.