We present observations with the INTEGRAL/IBIS telescope of the wind nebula powered by the young pulsar B1509-58 and we discuss the spatial and spectral properties of the unpulsed emission in the 20 - 200 keV energy band .
The source extension and orientation along the northwest-southeast axis corresponds to the jet emission seen at keV and TeV energies .
The hard X-ray spectrum is consistent with the earlier Beppo-SAX measurements .
It follows a power law with a photon index \alpha = -2.12 \pm 0.05 up to 160 keV .
A possible break at this energy is found at the 2.9 \sigma confidence level .
The 0.1-100 keV data are consistent with synchrotron aging of pairs in the jet and yield a magnetic field strength of 22-33 \mu G for a bulk velocity of 0.3-0.5c .
The synchrotron cut-off energy thus corresponds to a maximum electron energy of 400-730 TeV .