  The axial anomaly arising from the fermion sector of $\U(N)$ or $\SU(N)$
reduced model is studied under a certain restriction of gauge field
configurations (the ``$\U(1)$ embedding'' with $N=L^d$). We use the
overlap-Dirac operator and consider how the anomaly changes as a function of a
gauge-group representation of the fermion. A simple argument shows that the
anomaly vanishes for an irreducible representation expressed by a Young tableau
whose number of boxes is a multiple of $L^2$ (such as the adjoint
representation) and for a tensor-product of them. We also evaluate the anomaly
for general gauge-group representations in the large $N$ limit. The large $N$
limit exhibits expected algebraic properties as the axial anomaly.
Nevertheless, when the gauge group is $\SU(N)$, it does not have a structure
such as the trace of a product of traceless gauge-group generators which is
expected from the corresponding gauge field theory.
