The High Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory is an extensive air shower array located in Puebla, Mexico. The closest radio galaxy within the HAWC field of view, M87, has been detected in very high energies. In this work we report upper limits on the TeV $\gamma$-ray flux of the radio galaxy M87. At a distance of 16 Mpc, M87 is a supergiant elliptical galaxy located in the Virgo Cluster that has been observed from radio wavelengths to TeV $\gamma$-rays. Although a single-zone synchrotron self-Compton model has been successfully used to explain the spectral energy distribution of this source up to a few GeV, the $\gamma$-ray spectrum at TeV has been interpreted within different theoretical models. We discuss the implications of these upper limits on the hadronic interactions, as well as the number of neutrino events expected in the IceCube neutrino telescope.