The soft gamma repeater SGR 1806−20 is most famous for its giant flare from 2004, which yielded the highest gamma-ray flux ever observed on Earth. The flare emphasized the importance of determining the distance to the SGR, thus revealing the flare’s energy output, with implications on SGRs energy budget and giant flare rates. We analyse X-ray scattering echoes observed by Swift/X-Ray Telescope (XRT) following the 2006 August 6 intermediate burst of SGR 1806−20. Assuming positions and opacities of the molecular clouds along the line of sight from previous works, we derive direct constraints on the distance to SGR 1806−20, setting a lower limit of 9.4 kpc and an upper limit of 18.6 kpc (90 per cent confidence), compared with a 6–15 kpc distance range by previous works. This distance range matches an energy output of ≈1046 erg for the 2004 giant flare. We further use, for the first time, the X-ray echoes in order to study the dust properties in molecular clouds. Analysing the temporal evolution of the observed flux using a dust-scattering model, which assumes a power-law size distribution of the dust grains, we obtain a power-law index of −3.3+0.6−0.7 (1σ) and a lower limit of (2σ) on the dust maximal grain size, both conforming to measured dust properties in the diffused interstellar medium (ISM). We advocate future burst follow-up observations with Swift, Chandra and the planned NuSTAR telescopes, as means of obtaining much superior results from such an analysis.