For patients with type 1 diabetes mellitus, appropriate control of blood glucose concentrations is vital. Exercise is one of the disturbances that can affect these concentrations. Therefore, predictions in the presence of exercise are useful among others for model-based control methods, bolus calculators and educational tools. Although several models quantifying the effect of exercise are available, they generally include a high number of model parameters, which makes the identification a particularly challenging task, especially if only blood glucose measurements are available. In this paper, a new data-based minimal extension for existing models of the glucoregulatory system, which is able to account for the effect of exercise, is proposed. As observed from clinical data, for given exercise intensities and durations, the model does not depend on exercise intensity, making intensity measurements obsolete. Another main advantage is that this minimal extension involves the identification of only two additional scalar model parameters. The resulting model shows good agreement with the clinical data, and the obtained parameters are consistent between patients.