  We study impurity effects in the spin nematic phase of the $S=1/2$
$J_1$-$J_2$ frustrated spin chain under an external magnetic field by using the
infinite density matrix renormalization group and the bosonization. It is found
that local magnetization almost saturates around the impurity and the
entanglement entropy nearly vanishes at the corresponding bonds, not only when
the magnetic interactions near the impurity are weakened but also when they are
strengthened compared to those in the bulk. Then, we examine spin correlations
and Friedel oscillations induced by the impurity. The bosonization provides a
qualitative understanding of the characteristic behaviors of the magnetization.
We also discuss impacts of the impurity on experiments by focusing on NMR
spectra.
