  In SU(3) lattice QCD formalism, we propose a method to extract gauge fields
from link-variables analytically. With this method, we perform the first study
on effective mass generation of off-diagonal gluons and infrared Abelian
dominance in the maximally Abelian (MA) gauge in the SU(3) case. Using SU(3)
lattice QCD, we investigate the propagator and the effective mass of the gluon
fields in the MA gauge with U(1)$_3 \timesU(1)_8$ Landau gauge fixing. The
Monte Carlo simulation is performed on $16^4$ at $\beta$=5.7, 5.8 and 6.0 at
the quenched level. The off-diagonal gluons behave as massive vector bosons
with the approximate effective mass $M_{\mathrm{off}} \simeq
1.1-1.2\mathrm{GeV}$ in the region of $r =0.3-0.8$fm, and the propagation is
limited within a short range, while the propagation of diagonal gluons remains
even in a large range. In this way, infrared Abelian dominance is shown in
terms of short-range propagation of off-diagonal gluons. Furthermore, we
investigate the functional form of the off-diagonal gluon propagator. The
functional form is well described by the four-dimensional Euclidean Yukawa-type
function $e^{-m_{\rm off}r}/r$ with $m_{\rm off} \simeq 1.3-1.4\mathrm{GeV}$
for $r = 0.1- 0.8$ fm. This also indicates that the spectral function of
off-diagonal gluons has the negative-value region.
