The “ Mouse ” ( PWN G359.23 - 0.82 ) is a spectacular bow shock pulsar wind nebula , powered by the radio pulsar J1747 - 2958 . The pulsar and its nebula are presumed to have a high space velocity , but their proper motions have not been directly measured . Here we present 8.5 GHz interferometric observations of the Mouse nebula with the Very Large Array , spanning a time baseline of 12 yr. We measure eastward proper motion for PWN G359.23 - 0.82 ( and hence indirectly for PSR J1747 - 2958 ) of 12.9 \pm 1.8 mas yr ^ { -1 } , which at an assumed distance of 5 kpc corresponds to a transverse space velocity of 306 \pm 43 km s ^ { -1 } . Considering pressure balance at the apex of the bow shock , we calculate an in situ hydrogen number density of approximately 1.0 _ { -0.2 } ^ { +0.4 } cm ^ { -3 } for the interstellar medium through which the system is traveling . A lower age limit for PSR J1747 - 2958 of 163 _ { -20 } ^ { +28 } kyr is calculated by considering its potential birth site . The large discrepancy with the pulsar ’ s spin-down age of 25 kyr is possibly explained by surface dipole magnetic field growth on a timescale \approx 15 kyr , suggesting possible future evolution of PSR J1747 - 2958 to a different class of neutron star . We also argue that the adjacent supernova remnant G359.1 - 0.5 is not physically associated with the Mouse system but is rather an unrelated object along the line of sight .