The multi-strange baryon yields in Pb--Pb collisions have been shown to exhibit an enhancement relative to pp reactions. In this work, Ξ and Ω production rates have been measured with the ALICE experiment as a function of transverse momentum, pT, 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< pT< 7.2 GeV/c and 0.8 GeV/c< pT< 5 GeV/c, for Ξ and Ω 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 pT 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 pT 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-Pb. The yield of hyperons relative to charged pions is studied and compared with results from pp and Pb-Pb collisions. A statistical model is employed, which describes the change in the ratios with volume using a canonical suppression mechanism, in which the small volume causes a species- dependent relative reduction of hadron production. The calculations, in which the magnitude of the effect depends on the strangeness content, show good qualitative agreement with the data.