  The nearly isotropic distribution of the TeV-PeV neutrinos recently detected
by IceCube suggests that they come from sources at distance beyond our Galaxy,
but how far they are is largely unknown due to lack of any associations with
known sources. In this paper, we propose that the cumulative TeV gamma-ray
emission accompanying the production of neutrinos can be used to constrain the
distance of these neutrino sources, since the opacity of TeV gamma rays due to
absorption by the extragalactic background light (EBL) depends on the distance
that these TeV gamma rays have travelled. As the diffuse extragalactic TeV
background measured by \emph{Fermi} is much weaker than the expected cumulative
flux associated with IceCube neutrinos, the majority of IceCube neutrinos, if
their sources are transparent to TeV gamma rays, must come from distances
larger than the horizon of TeV gamma rays. We find that above 80\% of the
IceCube neutrinos should come from sources at redshift $z>0.5$. Thus, the
chance for finding nearby sources correlated with IceCube neutrinos would be
small. We also find that, to explain the flux of neutrinos under the TeV
gamma-ray emission constraint, the redshift evolution of neutrino source
density must be at least as fast as the the cosmic star-formation rate.
