Postseismic recovery within fault damage zones involves slow healing of coseismic fractures leading to permeability reduction and strength increase with time. To better understand this process, experiments were performed by long‐term fluid percolation with calcite precipitation through predamaged quartz‐monzonite samples subjected to upper crustal conditions of stress and temperature. This resulted in a P wave velocity recovery of 50% of its initial drop after 64 days. In contrast, the permeability remained more or less constant for the duration of the experiment. Microstructures, fluid chemistry, and X‐ray microtomography demonstrate that incipient calcite sealing and asperity dissolution are responsible for the P wave velocity recovery. The permeability is unaffected because calcite precipitates outside of the main flow channels. The highly nonparallel evolution of strength recovery and permeability suggests that fluid conduits within fault damage zones can remain open fluid conduits after an earthquake for much longer durations than suggested by the seismic monitoring of fault healing.