  The numerical renormalization group is used to study quantum entanglement in
the Kondo impurity model with a pseudogapped density of states
$\rho(\varepsilon)\propto|\varepsilon|^r$ ($r>0$) that vanishes at the Fermi
energy $\varepsilon=0$. The model features a Kondo-destruction quantum critical
point (QCP) separating a partially screened phase (reached for impurity-band
exchange couplings $J>J_c$) from a local-moment phase ($J<J_c$). The impurity
contribution $S_e^{imp}$ to the entanglement entropy between a region of radius
$R$ around the magnetic impurity and the rest of the host system reveals a
characteristic length scale $R^*$ that distinguishes a regime $R\ll R^*$ of
maximal critical entanglement from one $R\gg R^*$ of weaker entanglement.
Within each phase, $S_e^{imp}$ is a universal function of $R/R^*$ with a
power-law decay for $R/R^*\gg 1$. The entanglement length scale $R^*$ diverges
on approach to the QCP with a critical exponent that depends only on $r$.
