High-Voltage Monolithic Active Pixel Sensors (HV-MAPS) based on a 180 nm HV-CMOS process have been proposed to realize thin, fast and highly integrated pixel sensors. The MuPix7 prototype, fabricated in the commercial AMS H18 process, features a fully integrated on-chip readout, i.e. hit-digitization, zero suppression and data serialization. MuPix7 is the first fully monolithic HV-CMOS pixel sensor that has been tested for the use in high irradiation environments like HL-LHC. We present results from laboratory and test beam measurements of MuPix7 prototypes irradiated with neutrons (up to 5.0 × 1015 neq/cm2) and 24 GeV protons (up to 7.8 × 1015 protons/cm2) and compare the performance with non-irradiated sensors. At sensor temperatures of about 8 °C efficiencies of ≥90% at noise rates below 40 Hz per pixel are measured for fluences of up to 1.5 × 1015 neq/cm2. A time resolution better than 22 ns, expressed as Gaussian σ, is measured for all tested settings and sensors, even at the highest irradiation fluences. The data transmission at 1.25 Gbit/s and the on-chip PLL remain fully functional.