The Compact Muon Solenoid (CMS) experiment is expected to collect an integrated luminosity of 3000 fb−1 during the High Luminosity phase of the Large Hadron Collider (HL-LHC). This scenario comes with a high number of collisions per bunch crossing, and in turn, a high level of radiation for the innermost layer of the CMS tracker. Simulations estimate a 1 MeV neutron equivalent fluence, Φeq, of 2.3 × 1016 cm−2 at a distance of 2.8 cm from the collision point. The inner tracker of the CMS detector is required to withstand this range of fluence and maintain tracking performance. Planar pixel sensors with an active thickness of 150 μm and pixel sizes of 25 × 100 μm2 or 50 × 50 μm2 have been produced by Hamamatsu Photonics (HPK) and Fondazione Bruno Kessler (FBK). The sensors were bump bonded to the RD53A readout chip prototype. The sensor-chip modules were irradiated with 23 MeV protons to the 1 MeV neutron equivalent fluence of up to 2.4 × 1016 cm−2 at the Zyklotron AG (ZAG).Non-irradiated and irradiated modules were tested in the DESY II beam test facility. The spatial resolution as a function of the incidence angle and hit efficiency as a function of the bias voltage of the sensors were determined from these measurements. It is shown that for the highest fluence, the planar modules still reach 98% hit efficiency at bias voltages below 800 V.