The multi-strange baryon yields in Pb-Pb collisions have been shown to exhibit an enhancement relative to pp reactions. In this work, Xi and Omega production rates have been measured with the ALICE experiment as a function of transverse momentum, p(T), in p-Pb collisions at a centre-of-mass energy of,/sNN = 5.02 TeV. The results cover the kinematic ranges 0.6 GeV/c <p(T) <7.2 GeV/c and 0.8 GeV/c <p(T) <5 GeV/c, for E and S-2 respectively, in the common rapidity interval 0.5 <ycms <0. Multi -strange baryons have been identified by reconstructing their weak decays into charged particles. The p(T) spectra are analysed as a function of event charged -particle multiplicity, which in p-Pb collisions ranges over one order of magnitude and lies between those observed in pp and Pb-Pb collisions. The measured p -r distributions are compared to the expectations from a Blast -Wave model. The parameters which describe the production of lighter hadron species also describe the hyperon spectra in high multiplicity p-P