Correlations of same-sign charged pions are analysed using proton-lead collision data collected by the LHCb experiment at a nucleon-nucleon centre-of-mass energy of 5.02TeV, corresponding to an integrated luminosity of 1.06 nb(-1). Bose-Einstein correlations are observed in the form of an enhancement of pair production for same-sign charged pions with a small four-momentum difference. The dependence of the correlation radius and the intercept parameter on the reconstructed charged-particle multiplicity is investigated. The measured correlation radii scale linearly with the cube root of the reconstructed charged-particle multiplicity, being compatible with predictions of hydrodynamic models on the collision system evolution.