Self-interaction in the active neutrinos is studied in the literature to alleviate the $H_0$ tension. Similar self-interaction can also explain the observed dips in the flux of the neutrinos coming from the distant astro-physical sources in IceCube detectors. In contrast to the flavour universal neutrino interaction considered for solving the $H_0$ tension, which is ruled out from particle physics experiments, we consider flavour specific neutrino interactions. We show that the values of self-interaction coupling constant and mediator mass required for explaining the IceCube dips are inconsistent with the strong neutrino self-interactions preferred by the combination of BAO, HST and Planck data. However, the required amount of self-interaction between tau neutrinos ($ u_tau$) in inverted hierarchy for explaining IceCube dips is consistent with the moderate self-interaction region of cosmological bounds at 1-$sigma$ level. For the case of other interactions and hierarchies, the IceCube preferred amount of self-interaction is consistent with moderate self-interaction region of cosmological bounds at 2-$sigma$ level only.
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