The spin-web compound Cu3TeO6, belongs to an intriguing group of materials where magnetism is governed by 3d9 copper Cu2+ ions. This compound has been sparsely experimentally studied and we here present the first investigation of its local magnetic properties using muon-spin relaxation/rotation ({mu}+SR). Our results show a clear long-range 3D magnetic order below TN as indicated by clear zero-field (ZF) muon-precessions. At TN = 61.7 K a very sharp transition is observed in the weak transverse-field (wTF) as well as ZF data. Contrary to suggestions by susceptibility measurements and inelastic neutron scattering, we find no evidence for either static or dynamic (on the time-scale of {mu}+SR) spin-correlations above TN.
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