Mixed matrix membranes (MMMs), possessing high porosity, have received extensive attention for gas sensing applications. However, those with high flexibility and significant sensitivity are rare. In this work, we report on the fabrication of a novel membrane, using Cu3(HHTP)2 MOF (Cu-MOF) embedded in a polymer matrix. A solution comprising a homogenous suspension of poly-vinyl alcohol (PVA) and ionic liquid (IL), and Cu-MOF solid particles, was cast onto a petri dish to obtain a flexible membrane (215 μm in thickness). The sensor membrane (Cu-MOF/PVA/IL), characterized for its structure and morphology, was assessed for its performance in sensing against various test gases. A detection limit of 1 ppm at 23 °C (room temperature) for H2S was achieved, with a response time of 12 s. Moreover, (Cu-MOF/PVA/IL) sensor exhibited excellent repeatability, long-term stability, and selectivity towards H2S gas. The other characteristics of the (Cu-MOF/PVA/IL) sensor include high flexibility, low cost, low-power consumption, and easy fabrication technique, which nominate this sensor as a potential candidate for use in practical industrial applications.