High frequency (60 GHz) electron spin resonance (ESR) has been studied for the quantum critical system Mn_1-xFe_xSi (0 < x < 0.24) at temperatures up to 50 K by using the original experimental technique. The analysis of ESR line shape allowed detecting the full set of spectroscopic parameters (oscillating magnetization, line width and g factor). The violation of classical Korringa-type relaxation and scaling behavior of the ESR line width was found to a result from iron doping. Non-Fermi-liquid effects in the temperature dependence of the ESR line width observed at quantum critical points x= 0.11 and x^c = 0.24 are shown to be described quantitatively in the theory by Wölfle and Abrahams.