  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.
