The goal of this paper is to analyze the impact of a primary neutron source on the s-process nucleosynthesis in massive stars at halo metallicity. Recent stellar models including rotation at very low metallicity predict a strong production of primary N14. Part of the nitrogen produced in the H-burning shell diffuses by rotational mixing into the He core where it is converted to Ne22 providing additional neutrons for the s process. We present nucleosynthesis calculations for a 25 Msun star at [Fe/H] = -3, -4, where in the convective core He-burning about 0.8 % in mass is made of primary Ne22. The usual weak s-process shape is changed by the additional neutron source with a peak between Sr and Ba, where the s-process yields increase by orders of magnitude with respect to the yields obtained without rotation. Iron seeds are fully consumed and the maximum production of Sr, Y and Zr is reached. On the other hand, the s-process efficiency beyond Sr and the ratio Sr/Ba are strongly affected by the amount of Ne22 and by nuclear uncertainties, first of all by the Ne22(alpha,n)Mg25 reaction. Finally, assuming that Ne22 is primary in the considered metallicity range, the s-process efficiency decreases with metallicity due to the effect of the major neutron poisons Mg25 and Ne22. This work represents a first step towards the study of primary neutron source effect in fast rotating massive stars, and its implications are discussed in the light of spectroscopic observations of heavy elements at halo metallicity.