The minimal model of glucose-insulin dynamics is currently being used in several diabetes-related applications, such as investigating the glucose metabolism, and in the developments of model predictive controllers and fault detection techniques for automatic blood glucose control (i.e., artificial pancreas). Different approaches have been proposed to identify this model, but none of them is capable of providing guaranteed robust enclosures for its parameters, something very desired in applications such as the artificial pancreas, where robustness is paramount. This paper presents a novel approach for guaranteed set-membership parameter estimation of the minimal model based on the well-renowned Set Inversion via Interval Analysis (SIVIA) algorithm. Because the computational complexity of this algorithm is the main barrier for its applicability, an efficient vectorial implementation of SIVIA was employed. Clinical data from a standard intravenous glucose tolerance test were used to prove the validity of the presented approach. Finally, Modal Interval Analysis was used to reduce the numerical overestimation due to the dependency problem of interval arithmetic and significantly speeding up the computations.