Trogocytosis is a fast uptake of membranes and associated molecules from one cell by another. Trogocytosis between natural killer (NK) cells and tumors is already described, but the functional relevance of NK–tumor targets material exchange is unclear. We investigated whether the immunosuppressive molecule HLA‐G that is commonly expressed by tumors in vivo and known to block NK cytolytic function, could be transferred from tumor cells to NK cells, and if this transfer had functional consequences. We show that activated NK cells acquire HLA‐G1 from tumor cells, and that upon this acquisition, NK cells stop proliferating, are no longer cytotoxic, and behave as suppressor cells. Such cells can inhibit other NK cells' cytotoxic function and protect NK‐sensitive tumor cells from cytolysis. These data are the first demonstration that trogocytosis of HLA‐G1 can be a major mechanism of immune escape that acts through effector cells made to act as suppressor cells locally, temporarily, but efficiently. The broader consequences of membrane sharing between immune and non‐immune cells on the function of effectors and the outcome of immune responses are discussed.