  MMonochromatic neutrinos from dark matter annihilations ($\chi\chi\to
\nu\bar\nu$) are always produced in association with a gamma-ray spectrum
generated by electroweak bremsstrahlung. Consequently, these neutrino lines can
be searched for not only with neutrino detectors but also indirectly with
gamma-ray telescopes. Here, we derive limits on the dark matter annihilation
cross section into neutrinos based on recent Fermi-LAT and HESS data. We find
that, for dark matter masses above 200 GeV, gamma-ray data actually set the
most stringent constraints on neutrino lines from dark matter annihilation and,
therefore, an upper bound on the dark matter total annihilation cross section.
In addition, we point out that gamma-ray telescopes, unlike neutrino detectors,
have the potential to distinguish the flavor of the final state neutrino. Our
results indicate that we have already entered into a new era where gamma-ray
telescopes are more sensitive than neutrino detectors to neutrino lines from
dark matter annihilation.
