The transverse momentum distributions of the strange and double-strange hyperon resonances ( Sigma ( 1385)(+/-), Xi ( 1530)(0)) produced in p-Pb collisions at root s(NN) = 5.02 TeV were measured in the rapidity range -0.5 < yCMS < 0 for event classes corresponding to different charged-particle multiplicity densities, < dN(ch)/d eta(lab)> . The mean transverse momentumvalues are presented as a function of < dNch/d eta(lab)>, as well as a function of the particle masses and compared with previous results on hyperon production. The integrated yield ratios of excited to ground- state hyperons are constant as a function of < dN(ch)/d eta(lab)>. The equivalent ratios to pions exhibit an increase with < dN(ch)/ d eta(lab)>, depending on their strangeness content.