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 mF606W>28.6, mF110W>27.4 (Vega system), equivalent to reddening-corrected luminosity limits LF606W<5e28, LF110W<6e28 erg s-1 for a distance d=2 kpc, at 3sig confidence. This, in turn, imposes lower limits on the contemporaneous X-ray/optical flux ratio of 1100 and X-ray/near-infra-red flux ratio of 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.
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