Using the data from the Analyzer of Space Plasma and Energetic Atoms (ASPERA-3) experiment on board Mars Express and hybrid simulations, we have investigated the entry of protons into the Martian induced magnetosphere. We discuss one orbit on the dayside with observations of significant proton fluxes at altitudes down to 260 km on 27 February 2004. The protons observed below the induced magnetosphere boundary at an altitude of less than 700 km have energies of a few keV, travel downward, and precipitate onto the atmosphere. The measured energy flux and particle flux are 10^8–10^9 eV cm^−2 s^−1 and 10^5–10^6 H^+ cm^−2 s^−1, respectively. The proton precipitation occurs because the Martian magnetosheath is small with respect to the heated proton gyroradius in the subsolar region. The data suggest that the precipitation is not permanent but may occur when there are transient increases in the magnetosheath proton temperature. The higher-energy protons penetrate deeper because of their larger gyroradii. The proton entry into the induced magnetosphere is simulated using a hybrid code. A simulation using a fast solar wind as input can reproduce the high energies of the observed precipitating protons. The model shows that the precipitating protons originate from both the solar wind and the planetary exosphere. The precipitation extends over a few thousand kilometers along the orbit of the spacecraft. The proton precipitation does not necessarily correlate with the crustal magnetic anomalies.