By means of non-perturbative ab initio calculations, it is shown that paramagnetic closed-shell molecules are characterized by a strongly non-linear magnetic response, whose main feature consists of a paramagnetic-to-diamagnetic transition in a strong magnetic field. The physical origin of this phenomenon is rationalised on the basis of an analytical model based on molecular orbital theory. For the largest molecules considered here, the acepleiadylene dianion and the corannulene dianion, the transition field is of the order of 10³ T, about one order of magnitude larger than the magnetic field strength currently achievable in experimental settings. However, our simple model suggests that the paramagnetic-to-diamagnetic transition is a universal property of paramagnetic closed-shell systems in strong magnetic fields, provided no singlet–triplet level crossing occurs for fields smaller than the critical transition field. Accordingly, fields weaker than 100 T should suffice to trigger the predicted transition for systems whose size is still well within the (medium–large) molecular domain, such as hypothetical antiaromatic rings with less than one hundred carbon atoms.