The production of the Λ (1520) baryonic resonance has been measured at midrapidity in inelastic pp collisions at s=7TeV and in p–Pb collisions at sNN=5.02TeV for non-single diffractive events and in multiplicity classes. The resonance is reconstructed through its hadronic decay channel Λ (1520) → pK ^- and the charge conjugate with the ALICE detector. The integrated yields and mean transverse momenta are calculated from the measured transverse momentum distributions in pp and p–Pb collisions. The mean transverse momenta follow mass ordering as previously observed for other hyperons in the same collision systems. A Blast-Wave function constrained by other light hadrons (π, K, KS0, p, Λ) describes the shape of the Λ (1520) transverse momentum distribution up to 3.5GeV/c in p–Pb collisions. In the framework of this model, this observation suggests that the Λ (1520) resonance participates in the same collective radial flow as other light hadrons. The ratio of the yield of Λ (1520) to the yield of the ground state particle Λ remains constant as a function of charged-particle multiplicity, suggesting that there is no net effect of the hadronic phase in p–Pb collisions on the Λ (1520) yield.