In this letter, we present a nanophotonic device consisting of plasmonic nanopatch array (NPA) with integrated metal-organic framework (MOF) for enhanced infrared absorption gas sensing. By designing a gold NPA on a sapphire substrate, we are able to achieve enhanced optical field that spatially overlaps with the MOF layer, which can adsorb carbon dioxide (CO2) with high capacity. Experimental results show that this hybrid plasmonic-MOF device can effectively increase the infrared absorption path of on-chip gas sensors by more than 1100-fold. The demonstration of infrared absorption spectroscopy of CO2 using the hybrid plasmonic-MOF device proves a promising strategy for future on-chip gas sensing with ultra-compact size.