We study primordial magnetic field effects on the matter perturbations in the universe. We assume magnetic field generation prior to the big bang nucleosynthesis (BBN), i.e., during the radiation-dominated epoch of the universe expansion, but do not limit analysis by considering a particular magnetogenesis scenario. Contrary to previous studies, we limit the total magnetic field energy density and not the smoothed amplitude of the magnetic field at large (of the order of 1 Mpc) scales. We review several cosmological signatures, such as halo abundance, thermal Sunyaev-Zel'dovich effect, and Lyα data. For a cross-check, we compare our limits with that obtained through the cosmic microwave background faraday rotation effect and BBN. The limits range between 1.5 nG and 4.5 nG for nB in (- 3; -1.5).