Dwarf irregular galaxies (dIrrs), as rotationally-supported systems, have more re-
liable J-factor measurements than dwarf spheroidal galaxies and have received attention as
targets for dark matter detection in recent years. In this paper, we use 10 years of IceCube
muon-track data and an unbinned maximum-likelihood-ratio method to search for neutrino
signals beyond the background from the directions of 7 dIrrs, aiming to detect neutrinos pro-
duced by heavy annihilation dark matter. We do not detect any significant signal. Based on
such null results, we calculate the upper limits on the velocity-averaged annihilation cross
section for 1 TeV - 10 PeV dark matter. Our limits, although weaker than the strictest con-
straints in the literature in this mass range, are also a good complement to the existing results
considering the more reliable J-factor measurements of dIrrs.