The continuous development of urban areas around the world led to an increase in construction material use and demand, with concrete seeing significant market uptake. Although significant progress has been made to reduce the environmental impact of concrete, there is still a stringent need for improvement. One of the most widely used methods to reduce the environmental impact of the cement industry and the construction industry alike is the replacement of ordinary Portland cement (OPC) by supplementary cementitious materials (SCM). Aside from by-products of industry, SCMs could also come from natural sources. Taking into account the porous structure of zeolites and their contribution to the improvement of the mechanical and durability properties of cement-based materials, the analysis of pore structure in cement pastes incorporating micronized natural zeolite is deemed necessary. In this research, the OPC was replaced by zeolite in three different percentages: 10%, 20%, and 30% by mass. The evolution of pore structure was investigated by means of nuclear magnetic resonance relaxometry at the curing ages of 1, 7, and 28 days. The microstructure of cement pastes was assessed by scanning electron microscopy investigations at 1, 7, 14, 21, and 28 days. The obtained results show that smaller pore sizes are present in cement pastes containing zeolites during the first 7 days. However, at the age of 28 days, the reference mix exhibits a similar pore structure to the mix containing 10% micronized zeolite due to the presence of larger amounts of hydration products. Increasing the replacement percentage to 30% results in larger pores, as indicated by larger values of the relaxation time.