Nanofiltration (NF) membranes have been used for different applications in water treatment. In this work, we studied two facile surficial adhesive functionalization processes using polydopamine (pDA) and a metal–organic framework (MOFs) and investigated their individual and synergistic effects on membrane rejection, permeability, and antifouling properties. The copper MOF nanoparticles (Cu-MOF) were synthesized and incorporated with the pDA for surface coating of NF membranes using two different static (dip-coating) and dynamic (filtration-assisted) fabrication processes. All of the functionalized membranes were characterized completely, and the effects of pDA and Cu-MOF separately and together on the membrane physicochemical properties were identified. The results showed that the surface functionalization by only pDA enhanced the dye rejection from 22% (blank) to 98% (pDA-functionalized membrane). The dip-coating approach resulted in uniform polymerization of pDA on the membrane surface, while the filtration-assisted technique generated a deficient pDA layer. The incorporation of Cu-MOF into the pDA layer improved the permeability of the pDA-functionalized membrane by increasing the hydrophilicity of membranes and providing more water pathways due to the porous structure of MOFs. In addition, the molecular dynamics (MD) investigation of MOF-functionalized membranes revealed the role of embedded Cu-MOF charge repulsion mechanisms in the rejection of anionic and cationic dyes.