The notion of the Planckian dissipation is extended to the system of the Caroli-de Gennes-Matricon discrete energy levels in the vortex core of superconductors and fermionic superfluids. In this extension, the Planck dissipation takes place when the relaxation time τ is comparable with the quantum Heisenberg time tH = s important. The anomalous spectral flow of the energy levels along the chiral branch of the Caroli-de Gennes-Matricon states becomes important in the super-Planckian region, i.e. when τ < ΔE. Second, the Planck dissipation separates the laminar flow of the superfluid liquid at τ < ΔE and the vortex turbulence regime at τ > ΔE.