  Compared with that of standard dark matter halos, the density profile of the
recently proposed new kind of dark matter structure named ultracompact
minihalos (UCMHs) is steeper and its formation time is earlier. If the dark
matter is composed of weakly interactive massive particles (WIMP), the
potential signals, e.g. neutrinos, from UCMHs due to the dark matter
annihilation would be detected by IceCube/DeepCore or other detectors and such
signals would have a very useful complementarity of gamma rays observations. On
the other hand, the formation of UCMHs is related to primordial curvature
perturbations on the smaller scales. So constraints on the abundance of UCMHs
can be used to give a limit on the perturbations on these scales. In previous
works in the literature, the authors focused on the {\gamma}-ray signals from
UCMHs due to dark matter annihilation. In this work, we investigate the
neutrino signals from nearby UCMHs. Although no excess of neutrino signals the
dark matter annihilation has been observed, the constraints on the abundance of
UCMHs can be obtained and these constraints can be translated into the limit on
the primordial curvature perturbations on small scales.
