  Muon-neutrino elastic scattering on electrons is an observable neutrino
process whose cross section is precisely known. Consequently a measurement of
this process in an accelerator-based $\nu_\mu$ beam can improve the knowledge
of the absolute neutrino flux impinging upon the detector; typically this
knowledge is limited to $\sim$ 10% due to uncertainties in hadron production
and focusing. We have isolated a sample of 135 $\pm$ 17 neutrino-electron
elastic scattering candidates in the segmented scintillator detector of
MINERvA, after subtracting backgrounds and correcting for efficiency. We show
how this sample can be used to reduce the total uncertainty on the NuMI
$\nu_\mu$ flux from 9% to 6%. Our measurement provides a flux constraint that
is useful to other experiments using the NuMI beam, and this technique is
applicable to future neutrino beams operating at multi-GeV energies.
