Livestock production in the tropics contributes significantly to global greenhouse gas emissions, so better understanding the role of silvopastoral systems (SPS) in mitigating such emissions is necessary. The aim of this study was to evaluate the amounts of carbon stored in the biomass and soil organic carbon (SOC) components of a Leucaena leucocephala cum Panicum maximum silvopasture system (SPS) compared to a deciduous tropical forest (DTF), and a grass monoculture (GM) in Michoacán, Mexico. The above- and below-ground biomass were measured by destructive sampling in the SPS and GM, while previously reported allometric equations were used to quantify biomass stocks in the DTF. The SOC concentration up to 30 cm was determined by dry combustion method. The SPS and DTF contained more aboveground biomass (41.8 ± 3.30 and 36.7 ± 5.72 Mg DM ha−1) compared to GM (8.0 ± 0.76 Mg DM ha−1). However, the SPS exhibited greater belowground biomass (16.4 ± 1.95 Mg DM ha−1) than the other systems. The DTF had the highest SOC fraction in all depth classes with values ranging from 3.1 ± 0.07% to 3.7 ± 0.06%, respectively, compared to the other systems. The total carbon stocks in SPS was similar to DTF (120.7 ± 10.97 vs. 120.9 ± 6.38 Mg C ha−1) but was significantly higher than GM (78.2 ± 8.41 Mg C ha−1). In dry tropical conditions, SPS displays enormous potential for increasing biomass and soil carbon stocks compared to the GM and can thus be used as a greenhouse gas mitigation strategy in livestock production systems.