Catalytic oxidation of methane is critical for exhaust after-treatment systems where cold-start emissions and lean combustion still pose serious challenges. In this work, the effect of support materials on the complete catalytic oxidation of methane over palladium is studied in dry and wet conditions. A series of metal oxides (CeO2, ZrO2, n-SiO2) and mixed metal oxides (Zr0.65Ce0.35O2, Zr0.33Ce0.33/n-Si0.33O2, Zr0.66Ce0.17/n-Si0.17O2) supported Pd catalysts were synthesized, characterized and tested for methane oxidation. Pd/n-SiO2 was found to be highly active catalyst with the lowest initial (T10%) and final (T100%) conversion temperatures as compared to Pd supported on CeO2 and ZrO2. Methane combustion over mixed oxide supports, prepared with different ratios of Zr:Ce:Si, showed improved catalytic performance. Catalyst with equal ratios of Zr:Ce:Si (Pd/Zr0.33Ce0.33/n-Si0.33O2) showed similar performance to that of Pd/n-SiO2 with approximately ~8 (±2) °C higher light-off temperature. Additionally, cyclic wet (8 vol% H2O) and dry reactions were performed to evaluate the hydrothermal stability and activity regeneration when switching from wet to dry conditions. Optimal addition of ZrO2 and CeO2 to n-SiO2 resulted in higher stability of palladium catalyst over wide ranges of temperatures (350–600 °C). Catalysts were characterized by various analytical techniques, including TEM, XRD, XRF, N2-BET, O2-TPD, and CO chemisorption. TEM results demonstrate that mixed oxide support stabilized Pd nanoparticles, and n-SiO2 encapsulation prevented sintering and deactivation. Activity tests and characterization results demonstrate overall superior catalytic properties of Pd supported on Zr0.33Ce0.33/n-Si0.33O2. This catalyst can be quite promising for practical applications due to its high activity for total methane oxidation and excellent thermal stability.