We present a measurement of the top-quark mass using the full data set of Tevatron s√=1.96 TeV proton-antiproton collisions recorded by the CDF II detector, corresponding to an integrated luminosity of 8.7 fb−1. The analysis uses events with one semileptonic t or t¯ decay, but without detection of the electron or muon. We select events with significant missing transverse energy and multiple jets. We veto events containing identified electrons or muons. We obtain distributions of the top-quark masses and the invariant mass of the two jets from W-boson decays from data and compare these to templates derived from signal and background samples to extract the top-quark mass and the energy scale of the calorimeter jets with in situ calibration. A likelihood fit of the templates from signal and background events to the data yields the top-quark mass, Mtop=173.93±1.64(stat)±0.87(syst) GeV/c2. This result is the most precise measurement to date of the mass of the top quark in this event topology.