The world of energy is on the cusp of profound transformation. Hydrogen or hydrogen-containing fuel mixtures in the form of synthesis gas, as carriers of clean energy, will be in the short term among the most efficient solutions to pressing environmental problems, reducing the amount of greenhouse gases as well as pollution of cities and dependence on oil-based fuels. Carbon dioxide conversion of methane is the most promising method for the production of synthesis gas due to the simultaneous consumption of two greenhouse gases and, accordingly, a successful solution to environmental problems. Ni/Mn-based catalysts have been prepared by self-propagating high-temperature synthesis (SHS) for this process. The samples were characterized by X-ray diffraction, scanning electron microscopy, and nitrogen porosimetry. The effects of the catalysts’ composition on activity, selectivity, and product yield were investigated. The influence of the content of Ni, Mn on the behavior of catalysts has been established. Comparison of spinels with different component ratios showed that they have a defective structure. Non-stoichiometric spinels with highly defective catalyst structures were obtained due to very high heating and cooling rates during SHS. They work as active sites, which underlies the high activity of the catalysts.