We report broad-band Hubble Space Telescope imaging of the field of soft \gamma - ray repeater SGR 0418+5729 with ACS/WFC and WFC3/IR . Observing in two wide filters F606W and F110W , we find no counterpart within the positional error circle derived from Chandra observations , to limiting magnitudes m _ { F 606 W } > 28.6 , m _ { F 110 W } > 27.4 ( Vega system ) , equivalent to reddening-corrected luminosity limits L _ { F 606 W } < 5 \times 10 ^ { 28 } , L _ { F 110 W } < 6 \times 10 ^ { 28 } erg s ^ { -1 } for a distance d = 2 kpc , at 3- \sigma confidence . This , in turn , imposes lower limits on the contemporaneous X-ray/optical flux ratio of \simeq 1100 and X-ray/near-infra-red flux ratio of \simeq 1000 . We derive an upper limit on the temperature and/or size of any fall-back disk around the magnetar . We also compare the detection limits with observations of other magnetars .