  We consider a model where sterile neutrinos can propagate in a large
compactified extra dimension giving rise to Kaluza-Klein (KK) modes and the
standard model left-handed neutrinos are confined to a 4-dimensional spacetime
brane. The KK modes mix with the standard neutrinos modifying their oscillation
pattern. We examine former and current experiments such as CHOOZ, KamLAND, and
MINOS to estimate the impact of the possible presence of such KK modes on the
determination of the neutrino oscillation parameters and simultaneously obtain
limits on the size of the largest extra dimension. We found that the presence
of the KK modes does not essentially improve the quality of the fit compared to
the case of the standard oscillation. By combining the results from CHOOZ,
KamLAND and MINOS, in the limit of a vanishing lightest neutrino mass, we
obtain the stronger bound on the size of the extra dimension as ~ 1.0(0.6)
micrometer at 99% C. L. for normal (inverted) mass hierarchy. If the lightest
neutrino mass turn out to be larger, 0.2 eV, for example, we obtain the bound ~
0.1 micrometer. We also discuss the expected sensitivities on the size of the
extra dimension for future experiments such as Double CHOOZ, T2K and NOvA.
