Using a set of cosmological hydro-dynamical simulations, we constrained the properties of primordial magnetic fields by studying their impact on the formation and evolution of dwarf galaxies. We performed a large set of simulations (8 dark matter only and 72 chemo-hydrodynamical) including primordial magnetic fields through the extra density fluctuations they induce at small length scales (k >= 10 h Mpc(-1)) in the matter power spectrum. Our sample of dwarfs includes nine systems selected out of the initial (3.4 Mpc h(-1))(3) parent box, resimulated from z=200 to z=0 using a zoom-in technique and including the physics of baryons. We explored a wide variety of primordial magnetic fields with strength B-lambda ranging from 0.05 to 0.50 nG and magnetic energy spectrum slopes n(B) from -2.9 to -2.1. Strong magnetic fields characterized by a high amplitude (B-lambda=0.50, 0.20 nG with n(B)=-2.9) or by a steep initial power spectrum slope (n(B)=-2.1, -2.4, with B-lambda=0.05 nG) induce perturbations on mass scales from 10(7) to 10(9) M-circle dot. In this context emerging galaxies see their star formation rates strongly boosted. They become more luminous and metal rich than their counterparts without primordial magnetic fields. Such strong fields are ruled out by their inability to reproduce the observed scaling relations of dwarf galaxies. They predict that dwarf galaxies are at the origin of an unrealistically early reionization of the Universe and that they also overproduce luminous satellites in the Local Group. Weaker magnetic fields impacting the primordial density field at corresponding masses less than or similar to 10(6) M-circle dot, produce a large number of mini dark matter halos orbiting the dwarfs, however out of reach for current lensing observations. This study allows us, for the first time, to constrain the properties of primordial magnetic fields based on realistic cosmological simulations of dwarf galaxies.