Radioisotopes are indispensable agents in medical diagnosis and treatment, among which 62, 64Cu and 68Ga are medical isotopes widely used in positron emission tomography (PET) imaging. Experiments of generating these radioisotopes via laser-induced photonuclear reactions were performed on the XingGuangIII laser facility of the Laser Fusion Research Center (LFRC) at Mianyang. Large-charge (Q_e ~ 40 nC) MeV electron (e–) beams were generated with 100 TW picosecond (ps) laser pulses. The e– beams then impinge on a metal stack composed of Ta foil and activation plates (natural Cu and Ga2O3), producing high-energy bremsstrahlung radiations and isotopes 62, 64Cu and 68Ga, respectively. The characteristic emissions of the produced 62, 64Cu and 68Ga were off-line detected and the production yields of 62, 64Cu and 68Ga were obtained to be the order of 106 per laser shot. The dependence of radioisotope production efficiency (per e–) on electron temperature (T_e) is investigated through Geant4 simulations. It is found that the production efficiency increases with the T_e and then reaches a saturation value of 8 × 10−5 for 62Cu and 10–5 for 68Ga at T_e ~ 10 MeV. The prospect of producing medically isotopes 62, 64Cu and 68Ga is further evaluated by using table-top femtosecond laser system of high repetition. Considering a repetition rate of 100 Hz, it is expected that the activity can reach 0.2 GBq for 62Cu, 0.1 GBq for 64Cu and 0.05 GBq for 68Ga, respectively. Such activity would meet the required dose for clinical PET imaging, indicating the great potential to produce medical radioisotopes with an all-optical, high-repetition laser system.