  The local magnetic field induced by $\mu^{+}$ trapped at an interstitial site
in a chiral superconductor with $p$-wave symmetry, such as Sr$_2$RuO$_4$, is
discussed by solving the Bogoliubov-de Gennes equation on the two-dimensional
square lattice. In the model Hamiltonian, the effect of the trapped $\mu^{+}$
extracting the electrons at surrounding Ru sites is phenomenologically taken
into account as a non-magnetic impurity potential which locally destroys the
chiral superconducting order with $p$-wave symmetry giving rise to local
circulating current around $\mu^{+}$ site. It is shown that the size of the
induced local magnetic field in the case with periodic boundary condition is
far smaller compared to the case with open boundary condition without
$\mu^{+}$, in which the surface current induced by destruction of
superconducting order at the surface boundary gives contribution corresponding
to the intrinsic angular momentum of the order of $\hbar N_{\rm s}/2$, with
$N_{\rm s}$ being the number of superconducting electrons. This result
qualitatively explains why the magnetic field $\simeq0.5$G measured by $\mu$SR
in Sr$_2$RuO$_4$ is far smaller than the expected intrinsic magnetic field
$\simeq 50$G which is nearly the same as the lower critical field $H_{{\rm
c}1}\simeq 50$G.
