We construct an equation of state of strange quark matter in a strong magnetic field within a confining model. The confinement is modeled by means of the Richardson potential for quark-quark interaction modified suitably to account for a strong magnetic field. We compare our results for the equation of state and magnetization of matter to those derived within the MIT bag model. The differences between these models arise mainly due to the momentum dependence of the strong interaction between quarks in the Richardson model. Specifically, we find that the magnetization of strange quark matter in this model has much more pronounced de Haas-van Alfvén oscillations than in the MIT bag model, which is the consequence of the (static) gluon-exchange structure of the confining potential. © 2013 American Physical Society.