In spite of massive progress in oil–water separation, attributable to the use of advanced materials, the separation process faces challenges such as low permeance and fouling problems. Therefore, superwettable materials used in several fields are considered potential candidates for oily wastewater treatment. Metal–organic frameworks (MOFs) are receiving more and more interest in various separation applications due to their wide potential applications. Nevertheless, MOFs have been rarely explored for separating stabilized oil-in-water emulsions due to the difficulty in finding highly hydrolytic stable MOF candidates for this application. Furthermore, oil can clog water-stable materials owing to its high density, causing the degradation of MOF particles. As a result, there is a need to develop better MOF materials that can fulfill these requirements. Herein, we have explored Cr-soc-MOF-1 as a candidate for this application and deployed it as a membrane, which exhibited superhydrophilicity and underwater superoleophobicity for separating stabilized oil-in-water emulsions. The Cr-soc-MOF-1 membranes were synthesized by assembling the as-prepared MOF particles on a mixed cellulose ester substrate using a vacuum-assisted self-assembly technique. The Cr-soc-MOF-1 membrane exhibited ultrahigh water permeance (7465.9 L·m–2·h–1·bar–1), very high oil rejection (99.9%), and excellent anti-oil-fouling properties. The Cr-soc-MOF-1 membranes also exhibited excellent recyclability over 10 continuous separation cycles. Further, they exhibited an outstanding performance in separating various surfactant-stabilized oil-in-water emulsions. Thus, the Cr-soc-MOF-1 membranes exhibit a high potential in treating oily wastewater.