  We study effective mass generation of off-diagonal gluons and infrared
abelian dominance in the maximally abelian (MA) gauge. Using the SU(2) lattice
QCD, we investigate the propagator and the effective mass of the gluon field in
the MA gauge with the U(1)$_3$ Landau gauge fixing. The Monte Carlo simulation
is performed on the $12^3 \times 24$ lattice with $2.2 \le \beta \le 2.4$, and
also on the $16^4$ and $20^4$ lattices with $2.3 \le \beta \le 2.4$. In the MA
gauge, the diagonal gluon component $A_\mu^3$ shows long-range propagation, and
infrared abelian dominance is found for the gluon propagator. In the MA gauge,
the off-diagonal gluon component $A_\mu^\pm$ behaves as a massive vector boson
with the effective mass $M_{\rm off} \simeq 1.2$ GeV in the region of $r \gsim
0.2$ fm, and its propagation is limited within short range. We conjecture that
infrared abelian dominance can be interpreted as infrared inactivity of the
off-diagonal gluon due to its large mass generation induced by the MA gauge
fixing.
