Concrete is one of the most widely used construction materials all around the globe. Associated with urban expansion, concrete pavements increase the impermeable surfaces that affect the hydrological cycle and generate urban heat islands. Cement is one of the main components of concrete, and its production is one of the main sources of worldwide CO₂ emissions. Pervious concrete with partial cement replacement represents a more sustainable alternative. In this paper, the use of natural pozzolans zeolite and pumicite, as partial cement replacement materials in pervious concrete mixtures, is analyzed. The mechanical and hydraulic properties of pervious concretes using different percentages of pumicite and zeolite to replace cement (0% to 20%) were evaluated by a series of tests on compressive strength, flexural strength, permeability, porosity, and a microanalysis by SEM for the samples. Additionally, experiments with a plasticizer additive were conducted. The results show that mixtures with 0.35 W/C ratio present better mechanical and hydraulic properties; pumicite shows a better performance than zeolite, with the better properties achieved at 10% cement replacement; and the addition of plasticizer increased the final strengths. It is recommended to partially replace cement by adding 10% pumicite and to consider using 0.7% of plasticizer.