Preliminary results on the phi (1020) meson production in inelastic proton-proton collisions measured by the NA61/SHINE experiment at the CERN SPS are presented in these proceedings. The results include the first ever differential P-T and y measurements at beam momenta of 40 and 80 GeV and the most ever detailed experimental data at 158 GeV. The comparison of p + p to Pb + Pb results shows a non-trivial system size dependence of the widths of the rapidity distributions for phi mesons, contrasting with that of other hadrons. The results are furthermore compared to the world data on phi meson production, demonstrating the better accuracy achieved by the NA61/SHINE experiment, and to several models. None of the models is found to be able to describe simultaneously the shape of transverse momentum spectra, the shape of rapidity distribution and the total yield.