Nuclear fragmentation measurements are necessary when using heavy-ion beams in hadrontherapy to predict the effects of the ion nuclear interactions within the human body. Moreover, they are also fundamental to validate and improve the Monte Carlo codes for their use in planning tumor treatments. Nowadays, a very limited set of carbon fragmentation cross sections are being measured, and in particular, to our knowledge, no double-differential fragmentation cross sections at intermediate energies are available in the literature. In this work, we have measured the double-differential cross sections and the angular distributions of the secondary fragments produced in the (12)C fragmentation at 62 A MeV on a thin carbon target. The experimental data have been used to benchmark the prediction capability of the Geant4 Monte Carlo code at intermediate energies, where it was never tested before. In particular, we have compared the experimental data with the predictions of two Geant4 nuclear reaction models: the Binary Light Ions Cascade and the Quantum Molecular Dynamic. From the comparison, it has been observed that the Binary Light Ions Cascade approximates the angular distributions of the fragment production cross sections better than the Quantum Molecular Dynamic model. However, the discrepancies observed between the experimental data and the Monte Carlo simulations lead to the conclusion that the prediction capability of both models needs to be improved at intermediate energies.