Conventional wound dressings only protect passively against bacterial infection. Emerging mechanically active adhesive dressings (AADs) are inspired by the active closure of embryonic wounds. It can promote wound healing by actively contracting the wound bed. AADs meet the requirements of high toughness, stimulus–response, and dynamic adhesion properties, which are challenging. Hence, we construct a water-responsive shape memory polyurea fibrous membrane (PU-fm) featuring favorable toughness, wet-adhesion, breathability, absorbency of four times its weight, and antibacterial. First, the water-toughened electrospun PU-fm is fabricated using a homemade polyurea (PU) elastomer with multistage hydrogen bond networks as a spinning solution. Furthermore, a Janus-structured polyurea-polydopamine-silver fibrous membrane (PU@PDA@Ag-fm) is engineered, integrating antibacterial properties without compromising mechanical robustness. It demonstrates strong adhesion to the skin, actively promotes wound contraction, and enables adaptive wrapping of tissues of varying sizes by the water-driven shape memory effect. Antibacterial tests and wound healing experiments indicate that the PU@PDA@Ag-fm has favorable antibacterial properties against Escherichia coli (E.coli) and accelerates the wound healing rate by 20%. For the first time, water-responsive shape memory PU-fm as the AADs is constructed, providing a new strategy for wound management. This can be extended to applications in other smart devices for biomedicine such as tendon repair, and bioelectronic interfaces.