We report on an analysis of the high-energy muon component in near-vertical extensive air showers detected by the surface array IceTop in coincidence with the in-ice array of the IceCube Neutrino Observatory. In the coincidence measurement, the predominantly electromagnetic signal measured by IceTop is used to estimate the cosmic-ray primary energy, and the energy loss of the muon bundle in the deep in-ice array is used to estimate the number of muons in the shower with energies above 500 GeV (“TeV muons”). The average multiplicity of these TeV muons is determined for cosmic-ray energies between 2.5 PeV and 100 PeV assuming three different hadronic interaction models: Sibyll 2.1, QGSJet-II.04, and EPOS-LHC. For all models considered, the results are found to be in good agreement with the expectations from simulations. A tension exists, however, between the high-energy muon multiplicity and other observables; most importantly the density of GeV muons measured by IceTop using QGSJet-II.04 and EPOS-LHC.