The effect of pressure on the Neel temperature (TN) and on the temperature dependence of the magnetic susceptibility of a helicoidal ferromagnetic MnSi was analyzed as part of the LDA+U-model augmented with the account of the relativistic antisymmetric Dzyaloshinskii-Moriya interaction. It was shown that the Fermi level is in the area of DOS local minimum. This causes instability of magnetic solutions and the occurrence of higher amplitude zero spin fluctuations simulating the pattern of local magnetic moments. An increase in temperature-dependent spin-fluctuation effects with an increase in pressure leads to a decrease in TN. As a result, at pressures above 14.45 kbar, zero spin fluctuations are retained over the entire temperature range below TN. After disappearance of helicoidal ferromagnetism, a paramagnetic state occurs where the effect of the abrupt suppression of local magnetic moments takes place upon a temperature increase.