  We study nonperturbative corrections to the transverse momentum distribution
of vector bosons in the Drell-Yan process. Factorizing out the Sudakov effects
due to soft gluons we express their contribution to the distribution in the
form of the vacuum averaged Wilson loop operator. We calculate the
nonperturbative contribution to the Sudakov form factor using the expansion of
the Wilson loop over vacuum fields supplemented with the expression for
nonlocal gauge invariant field strength correlator. Although the Wilson loop is
defined in an essentially Minkowski kinematics, the part of the nonperturbative
contribution depending on the invariant mass of the produced vector bosons is
governed by asymptotics of the correlator at large space-like (Euclidean)
separations and therefore can be calculated using conventional nonperturbative
methods. Applying the results of lattice calculations we found that the
obtained expression for the nonperturbative power corrections is in qualitative
agreement with known phenomenological expressions at large transverse momenta
and deviate from them at small transverse momenta.
