Highly sensitive and selective methane (CH4) gas detection is a critical challenge in complex practical scenarios. Herein, this work presents an excellent CH4 gas sensor based on ZnO/Pd nanorods encapsulated in a zeolitic imidazolate framework (ZIF)-7 shell. Compared with the ZnO/Pd sensor, the ZnO/Pd@ZIF-7 sensor exhibited a faster response/recovery time (2.3/8.3 s) and higher response (668.5%) toward 5000 ppm of CH4 gas at 180 °C. Furthermore, a 22-fold higher selectivity to CH4 against ethanol (C2H5OH) was observed. The improved sensitivity and selectivity of the ZnO/Pd@ZIF-7 sensor are attributed to the dual roles played by the ZIF-7 shell; first, it generates more chemisorbed oxygen on the ZnO surface while improving the catalytic activity of Pd, and it facilitates the catalytic oxidation of CH4 and ultimately improves the sensitivity. Moreover, the ZIF-7 shell has filtering effects, which significantly reduces the response of interfering gases and exhibits excellent CH4 selectivity. This paper explores the strategy of combining a dual-functional ZIF-7 shell with ZnO/Pd, proposing a gas sensor design concept that broadens the application of metal–organic framework materials for CH4 detection.