  The presence of magnetic fields in the early universe affects the
cosmological processes, leading to the distinct signature, which allows
constraining their properties and the genesis mechanisms. In this study, we
revisit the method to constrain the amplitude of the magnetic fields on small
scales in the radiation-dominated era from the abundance of primordial black
holes. Constraints in the previous work were based on the fact that the density
perturbations sourced by stronger magnetic fields become large enough to
gravitationally collapse to form PBHs. However, we demonstrate that this
picture is incomplete because magnetic fields also increase the threshold value
of the density contrast required for PBH formation. The increase in threshold
density contrast is more pronounced on smaller scales, and in extreme cases, it
might even prevent PBH production despite the presence of significant magnetic
field. Taking into account the relevant physical effects on the magnetized
overdense region, we establish an upper-limit on the amplitude of comoving
magnetic fields, approximately $0.12-0.14 {\rm \mu G}$ at a scale of $10^{17}
{\rm Mpc}^{-1}$. Additionally, we compare our constraints with various
small-scale probes.
