Chirality of matter can produce unique responses in optics, electricity and magnetism. In particular, magnetic crystals transmit their handedness to the magnetism via antisymmetric exchange interaction of relativistic origin, producing helical spin orders as well as their fluctuations. Here we report for a chiral magnet MnSi that chiral spin fluctuations manifest themselves in the electrical magnetochiral effect (eMChE), i.e. the nonreciprocal and nonlinear response characterized by the electrical conductance depending on inner product of electric and magnetic fields $\boldsymbol{E} ⋅ \boldsymbol{B}$. Prominent eMChE signals emerge at specific temperature-magnetic field-pressure regions: in the paramagnetic phase just above the helical ordering temperature and in the partially-ordered topological spin state at low temperatures and high pressures, where thermal and quantum spin fluctuations are conspicuous in proximity of classical and quantum phase transitions, respectively. The finding of the asymmetric electron scattering by chiral spin fluctuations may explore new electromagnetic functionality in chiral magnets. ; Comment: 25 pages, 9 figures (including Supplementary Information)