We calculate the low-temperature superheating field $B_{\rm sh}$ of clean superconductors near the boundary between type-I and type-II superconductivity, with particular emphasis on Nb. Ginzburg–Landau theory is not applicable at low temperatures, while previous microscopic calculations have been limited to either the large-$\kappa$ regime or the dirty limit. The clean, low-$\kappa$ regime relevant to Nb has therefore remained unresolved. We solve the self-consistent nonlinear nonlocal Eilenberger problem for the Meissner state and then analyze its stability against small perturbations. For a Nb-like material with $\kappa_{\rm GL}=0.7$, we obtain $B_{\rm sh}\simeq290\,{\rm mT}$ at $T/T_c=0.2$, using $B_{c0}\simeq200\,{\rm mT}$. For a TESLA-shaped Nb accelerator cavity, this corresponds to an intrinsic Meissner-stability limit of about $67\,{\rm MV/m}$.