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 ($k geq 10,h,rm{Mpc^{-1}}$) in the matter power spectrum. We explored a large variety of primordial magnetic fields with strength $B_lambda$ ranging from $0.05$ to $0.50,textrm{nG}$ and magnetic energy spectrum slopes $n_B$ from $-2.9$ to $-2.1$. Strong magnetic fields characterized by a high amplitude ($B_lambda=0.50,,0.20,textrm{nG}$ with $n_B=-2.9$) or by a steep initial power spectrum slope ($n_B=-2.1,-2.4$, with $B_lambda=0.05,textrm{nG}$) induce perturbations in the mass scales from $10^7$ to $10^9,rm{M}_{odot}$. In this context emerging galaxies see their star formation rate 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 dwarf galaxies to be at the origin of an unrealistically early reionization of the Universe and also overproduce luminous satellites in the Local Group. Weaker magnetic fields impacting the primordial density field at corresponding masses $lesssim 10^6,rm{M}_{odot}$, produce a large number of mini dark halos orbiting the dwarfs, however out of reach for current lensing observations. This study allows for the first time to constrain the properties of primordial magnetic fields based on realistic cosmological simulations of dwarf galaxies.
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