Enzyme replacement therapy shows remarkable clinical improvement in treating lysosomal storage disorders. However, this therapeutic approach is hampered by limitations in the delivery of the enzyme to cells and tissues. Therefore, there is an urgent, unmet clinical need to develop new strategies to enhance the enzyme delivery to diseased cells. Graphene-based materials, due to their dimensionality and favourable pattern of interaction with cells, represent a promising platform for the loading and delivery of therapeutic cargo. Herein, the potential use of graphene-based materials, including defect-free graphene with positive or negative surface charge and graphene oxide with different lateral dimensions, was investigated for the delivery of lysosomal enzymes in fibroblasts derived from patients with Mucopolysaccharidosis VI and Pompe disease. We report excellent biocompatibility of all graphene-based materials up to the concentration of 100 g/mL in the cell lines studied. In addition, a noticeable difference in the uptake profile of the materials was observed. Neither type of graphene oxide was taken up by the cells to a significant extent. In contrast, the two types of graphene were efficiently taken up, localizing in the lysosomes. Furthermore, we demonstrate that cationic graphene flakes can be used as carriers for arylsulfatase B enzyme, for the delivery of the lacking enzyme to the lysosomes of Mucopolysaccharidosis VI fibroblasts. Graphene complexed arylsulfatase B not only retained enzyme activity, but also exerted biological effect almost twice as higher than arylsulfatase B in the clearance of the substrate in Mucopolysaccharidosis VI fibroblasts. This study lays the groundwork for the potential use of graphene-based material as carriers for enzyme replacement therapy in lysosomal storage disorders.