The ratio of the deuteron to proton structure functions is measured at very small Bjorken $x$ (down to 1${0}^{--6}$) and for ${Q}^{2}>0.001$ Ge${\mathrm{V}}^{2}$ from scattering of 470 GeV muons on liquid hydrogen and deuterium targets. The ratio ${F}_{2}^{n}{/F}_{2}^{p}$ extracted from these measurements is found to be constant, at a value of $0.935\ifmmode\pm\else\textpm\fi{}0.008\ifmmode\pm\else\textpm\fi{}0.034$, for $x<0.01$. This result suggests the presence of nuclear shadowing effects in the deuteron. The dependence of the ratio on ${Q}^{2}$ is also examined; no significant variation is found.
