In this study, we carried out an investigation of the etching characteristics(etch rate, selectivity) of $HfO_2$ thin films in the $CH_4/Ar$ inductively coupled plasma. It was found that variations of input power and negative dc-bias voltage are investigated by the monotonic changes of the $HfO_2$ etch rate as it generally expected from the corresponding variations of plasma parameters. At the same time, a change in either gas pressure or in gas mixing ratio result in non-monotonic etch rate that reaches a maximum at 2 Pa and for $CH_4(20%)/Ar(80%)$ gas mixture, respectively. The X-ray photoelectron spectroscopy analysis showed an efficient destruction of the oxide bonds by the ion bombardment as well as showed an accumulation of low volatile reaction products on the etched surface. Based on these data, the ion-assisted chemical reaction was proposed as the main etch mechanism for the $CH_4-containing$ plasmas.