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In this work, we propose an approach to determine the dosages of antithyroid agents to treat hyperthyroid patients. Instead of relying on a trial-and-error approach as it is commonly done in clinical practice, we suggest to determine the dosages by means of a model predictive control (MPC) scheme. To this end, we first extend a mathematical model of the pituitary-thyroid feedback loop such that the intake of methimazole, a common antithyroid agent, can be considered. Second, based on the extended model, we develop an MPC scheme to determine suitable dosages. In numerical simulations, we consider scenarios in which (i) patients are affected by Graves' disease and take the medication orally and (ii) patients suffering from a life-threatening thyrotoxicosis, in which the medication is usually given intravenously. Our conceptual study suggests that determining the medication dosages by means of an MPC scheme could be a promising alternative to the currently applied trial-and-error approach.