The aim of this study is to evaluate the geomagnetically induced current (GIC) hazard in the power networks of the Canary and Balearic archipelagos. This is done in order to strictly complete the detailed assessment at national level of the power transmission system of mainland Spain, including the 400 and 220 kV levels. We have constructed models for the grids in each of the individual systems and used resistivity models of the lithosphere for each group of islands, from which we have calculated the surface impedances. The respective models of electrical admittances of the grids have been combined with the geoelectric field derived from the convolution of the recorded (or expected in an extreme scenario) geomagnetic storms and the impedances calculated from the geoelectrical models to derive the expected GICs in the power lines, substations, and transformers. The low geomagnetic latitude of the Canary Islands combined with the small size of their power networks, makes them one of the least likely electrified locations to record significant GICs, with less than 3 A for the 100‐year return period. Even the 13 A that could be reached for the upper limit of the 95% confidence interval at the 500‐year return period does not seem likely to have a significant impact. The Balearic Islands, being at higher latitude and with a system length of approximately 300 km, including alternating current power lines connecting the Islands, shows GIC signals of moderate amplitude with up to 40 A for the 100‐year return period.