To explore cellular responses to high magnetic fields (HMF), we present a model of the interactions of cells with a homogeneous HMF that accounts for the magnetic force exerted on paramagnetic/diamagnetic species. There are various chemical species inside a living cell, many of which may have large concentration gradients. Thus, when an HMF is applied to a cell, the concentration-gradient magnetic forces act on paramagnetic or diamagnetic species and can either assist or oppose large particle movement through the cytoplasm. We demonstrate possibilities for changing the machinery in living cells with HMFs and predict two new mechanisms for modulating cellular functions with HMFs via (i) changes in the membrane potential and (ii) magnetically assisted intracellular diffusiophoresis of large proteins. By deriving a generalized form for the Nernst equation, we find that an HMF can change the membrane potential of the cell and thus have a significant impact on the properties and biological functionality of cells. The elaborated model provides a universal framework encompassing current studies on controlling cell functions by high static magnetic fields. Bioelectromagnetics. 2021;42:27-36. © 2020 Bioelectromagnetics Society.