Background: Geant4 is a Monte Carlo code extensively used in medical physics for a wide range of applications, such as dosimetry, micro- and nanodosimetry, imaging, radiation protection, and nuclear medicine. Geant4 is continuously evolving, so it is crucial to have a system that benchmarks this Monte Carlo code for medical physics against reference data and to perform regression testing. Aims: To respond to these needs, we developed G4-Med, a benchmarking and regression testing system of Geant4 for medical physics. Materials and Methods: G4-Med currently includes 18 tests. They range from the benchmarking of fundamental physics quantities to the testing of Monte Carlo simulation setups typical of medical physics applications. Both electromagnetic and hadronic physics processes and models within the prebuilt Geant4 physics lists are tested. The tests included in G4-Med are executed on the CERN computing infrastructure via the use of the geant-val web application, developed at CERN for Geant4 testing. The physical observables can be compared to reference data for benchmarking and to results of previous Geant4 versions for regression testing purposes. Results: This paper describes the tests included in G4-Med and shows the results derived from the benchmarking of Geant4 10.5 against reference data. Discussion: Our results indicate that the Geant4 electromagnetic physics constructor G4EmStandardPhysics_option4 gives a good agreement with the reference data for all the tests. The QGSP_BIC_HP physics list provided an overall adequate description of the physics involved in hadron therapy, including proton and carbon ion therapy. New tests should be included in the next stage of the project to extend the benchmarking to other physical quantities and application scenarios of interest for medical physics. Conclusion: The results presented and discussed in this paper will aid users in tailoring physics lists to their particular application.