In this study, a polyamide forward osmosis membrane was functionalized with zwitterions followed by the in situ growth of metal–organic frameworks with silver as a metal core (Ag-MOFs) to improve its antibacterial and antifouling activity. First, 3-bromopropionic acid was grafted onto the membrane surface after its activation with N,N-diethylethylenediamine. Then, the in situ growth of Ag-MOFs was achieved by a simple membrane immersion sequentially in a silver nitrate solution and in a ligand solution (2-methylimidazole), exploiting the underlying zwitterions as binding sites for the metal. The successful membrane functionalization and the enhanced surface wettability were verified through an array of characterization techniques. When evaluated in forward osmosis tests, the modified membranes exhibited high performance and improved permeability compared to pristine membranes. Static antibacterial experiments, evaluated by confocal microscopy and colony-forming unit plate count, resulted in a 77% increase in the bacterial inhibition rate due to the activity of the Ag-MOFs. Microscopy micrographs of the Escherichia coli bacteria suggested the deterioration of the biological cells. The antifouling properties of the functionalized membranes translated into a significantly lower flux decline in forward osmosis filtrations. These modified surfaces displayed negligible depletion of silver ions over 30 days, confirming the stable immobilization of Ag-MOFs on their surface.