We report a direct detection of muon-induced high-energy neutrons with a 12-liter neutron detector fabricated with EJ-301 liquid scintillator operating at Soudan mine for about two years. The detector response to energy from a few MeV up to $\ensuremath{\sim}20\text{ }\text{ }\mathrm{MeV}$ has been calibrated using radioactive sources and cosmic-ray muons. Subsequently, we have calculated the scintillation efficiency for nuclear recoils, up to a few hundred MeV, using Birks' law in the Monte Carlo simulation. Data from an exposure of 655.1 days were analyzed and neutron-induced recoil events were observed in the energy region from 4 to 50 MeV, corresponding to fast neutrons with kinetic energy up to a few hundred MeV, depending on the scattering angle. Combining with the Monte Carlo simulation, the measured muon-induced fast neutron flux is determined to be $(2.23\ifmmode\pm\else\textpm\fi{}0.52(\text{sta})\ifmmode\pm\else\textpm\fi{}0.99(\text{sys}))\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ (${E}_{n}\text{ }>20\text{ }\text{ }\mathrm{MeV}$), in a reasonable agreement with the model prediction. The muon flux is found to be ($1.65\ifmmode\pm\else\textpm\fi{}0.02(\text{sta})\ifmmode\pm\else\textpm\fi{}0.1(\text{sys}))\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0ex}{0ex}}{10}^{\ensuremath{-}7}\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ (${E}_{\ensuremath{\mu}}\text{ }>1\text{ }\text{ }\mathrm{GeV}$), consistent with other measurements. As a result, the muon-induced high-energy gamma-ray flux is simulated to be $7.08\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ (${E}_{\ensuremath{\gamma}}\text{ }>\text{ }1\text{ }\text{ }\mathrm{MeV}$) for the depth of Soudan.