Magnetism induced by defects in nominally non-magnetic solids has attracted intense scientific interest in recent years. The local magnetism in highly disordered undoped and Co-doped topological insulator (TI) Bi2Se3 nanoplates has been investigated by muon spin relaxation (μSR). Using μSR spectroscopy, together with other macroscopic characterizations, we find that these nanoplates are composed of a core with both static fields and dynamically fluctuating moments, and a shell with purely dynamically fluctuating moments. The fluctuations in the core die out at low temperatures, while those in the shell continue till 2 K. When Bi2Se3 is doped with Co, the static magnetic component increases, whilst keeping the dual (static-plus-dynamic) nature intact. The findings indicate that highly disordered TI’s could constitute a new class of promising magnetic materials that can be engineered by magnetic impurity doping.