A measurement of the inclusive b-jet production cross section is presented in pp and p-Pb collisions at sNN = 5.02 TeV, using data collected with the ALICE detector at the LHC. The jets were reconstructed in the central rapidity region |η| < 0.5 from charged particles using the anti-kT algorithm with resolution parameter R = 0.4. Identification of b jets exploits the long lifetime of b hadrons, using the properties of secondary vertices and impact parameter distributions. The pT-differential inclusive production cross section of b jets, as well as the corresponding inclusive b-jet fraction, are reported for pp and p-Pb collisions in the jet transverse momentum range 10 ≤ pT,ch jet≤ 100 GeV/c, together with the nuclear modification factor, RpPbb−jet. The analysis thus extends the lower pT limit of b-jet measurements at the LHC. The nuclear modification factor is found to be consistent with unity, indicating that the production of b jets in p-Pb at sNN = 5.02 TeV is not affected by cold nuclear matter effects within the current precision. The measurements are well reproduced by POWHEG NLO pQCD calculations with PYTHIA fragmentation.