The observation of a radioactively-powered kilonova associated with the first binary neutron star (BNS) merger detected in gravitational waves proved that these events are ideal sites for the production of heavy r-process elements. However, the physical origin of the ejected material responsible for the early ("blue") and late ("red") components of this kilonova is still debated. Here, we investigate the possibility that the early/blue kilonova originated from the magnetically driven baryon wind launched after merger by the metastable neutron star remnant. Exploiting a magnetized BNS merger simulation with over 250 ms of post-merger evolution, we can follow for the first time the full mass ejection process up to its final decline. We find that the baryon wind carries ≃0.010−0.028M⊙ of unbound material, proving that the high mass estimated for the blue kilonova can be achieved. The expansion velocities of up to 0.2 c are marginally consistent with the observational estimates and we discuss various effects neglected here that could further improve the current agreement. Overall, our results show that the magnetically driven baryon wind is a viable explanation for the blue kilonova.