The application of gas-liquid membrane contactors for ethane-ethylene separation seems to offer a good alternative to conventional energy-intensive processes. This work aims to develop new hydrophobic composite membranes with active ethylene carriers and to demonstrate their potential for ethylene/ethane separation in gas-liquid membrane contactors. For the first time, hybrid membrane materials based on polyoctylmethylsiloxane (POMS) and silver tetrafluoroborate, with a Si:Ag ratio of 10:0.11 and 10:2.2, have been obtained. This technique allowed us to obtain POMS-based membranes with silver nanoparticles (8 nm), which are dispersed in the polymer matrix. The dispersion of silver in the POMS matrix is confirmed by the data IR-spectroscopy, wide-angle X-ray diffraction, and X-ray fluorescence analyses. These membranes combine the hydrophobicity of POMS and the selectivity of silver ions toward ethylene. It was shown that ethylene sorption at 600 mbar rises from 0.89 cm3(STP)/g to 3.212 cm3(STP)/g with an increase of Ag content in POMS from 0 to 9 wt%. Moreover, the membrane acquires an increased sorption affinity for ethylene. The ethylene/ethane sorption selectivity of POMS is 0.64; for the membrane with 9 wt% silver nanoparticles, the ethylene/ethane sorption selectivity was 2.46. Based on the hybrid material, POMS-Ag, composite membranes were developed on a polyvinylidene fluoride (PVDF) porous support, with a selective layer thickness of 5–10 µm. The transport properties of the membranes were studied by separating a binary mixture of ethylene/ethane at 20/80% vol. It has been shown that the addition of silver nanoparticles to the POMS matrix leads to a decrease in the ethylene permeability, but ethylene/ethane selectivity increases from 0.9 (POMS) to 1.3 (9 wt% Ag). It was noted that when the POMS-Ag membrane is exposed to the gas mixture flow for 3 h, the selectivity increases to 1.3 (0.5 wt% Ag) and 2.3 (9 wt% Ag) due to an increase in ethylene permeability. Testing of the obtained membranes in a gas-liquid contactor showed that the introduction of silver into the POMS matrix makes it possible to intensify the process of ethylene mass transfer by more than 1.5 times.