We present a series of controlled fluid injection experiments in the laboratory on a pre‐stressed natural rough fracture with a high initial permeability (∼10 −13 m 2 ) in granite using different fluid pressurization rates. Our results show that fluid injection on a fracture with a slight velocity‐strengthening frictional behavior exhibits dilatant slow slip in association with a permeability increase up to ∼41 times attained at the maximum slip velocity of 0.085 mm/s for the highest‐rate injection case. Under these conditions, the slip velocity‐dependent change in hydraulic aperture is a dominant process to explain the transient evolution of fracture permeability, which is modulated by fluid pressurization rate and fracture surface asperities. This leads to the conclusion that permeability evolution can be engineered for subsurface geoenergy applications by controlling the fluid pressurization rate on slowly slipping fractures.