  Primordial magnetic fields (PMFs) offer a compelling explanation for the
origin of observed magnetic fields, especially on extragalactic scales. Such
PMFs give rise to excess of power in small scale matter perturbations that
could strongly influence structure formation. We study the impact of the
magnetically enhanced matter power spectrum on the signal that will be observed
by line-intensity mapping (LIM) surveys targeting carbon monoxide (CO) emission
from star-forming galaxies at high redshifts. Specifically, the voxel intensity
distribution of intensity maps provides access to small-scale information,
which makes it highly sensitive to signatures of PMFs on matter overdensities.
We present forecasts for future LIM CO surveys, finding that they can constrain
PMF strength as small as $B_{\rm 1Mpc}\sim0.006-1\,{\rm nG}$, depending on the
magnetic spectral index and the targeted redshifts.
