Glucan phosphatases are members of a functionally diverse family of dual-specificity phosphatase (DSP) enzymes. The plant glucan phosphatase Starch Excess4 (SEX4) binds and dephosphorylates glucans, contributing to processive starch degradation in the chloroplast at night. Little is known about the complex kinetics of SEX4 when acting on its complex physiologically relevant glucan substrate. Therefore, we explored the kinetics of SEX4 against both insoluble starch and soluble amylopectin glucan substrates. SEX4 displays robust activity and a unique sigmoidal kinetic response to amylopectin, characterized by a Hill coefficient of 2.77 ± 0.63, a signature feature of cooperativity. We investigated the basis for this positive kinetic cooperativity and determined that the SEX4 carbohydrate-binding module (CBM) dramatically influences the binding cooperativity and substrate transformation rates. These findings provide insights into a previously unknown but important regulatory role for SEX4 in reversible starch phosphorylation and further advances our understanding of atypical kinetic mechanisms.