We propose a new type of optomagnetic effect induced by a highly confined plasmonic field in a nanocavity. It is shown that a very large dynamic magnetic field can be generated as the result of the inhomogeneity of nanocavity plasmons, which can directly activate spin-forbidden transitions in molecules. The dynamic optomagnetic effects on optical transitions between states of different spin multiplicities are illustrated by first-principles calculations for C60. Remarkably, the intensity of spin forbidden singlet-to-triplet transitions can even be stronger than that of singlet-to-singlet transitions when the spatial distribution of plasmon is comparable with the molecular size. This approach not only offers a powerful optomagnetic means to rationally fabricate molecular excited states with different multiplicities but also provides a groundbreaking concept of the light-matter interaction that could lead to the observation of new physical phenomena and the development of new techniques.