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One of the wajib acts of the prayer, is ‘qara’at’ (recitation). It is wajib in prayer to verbalize the words and it isn't enough to only pass them through the mind. There is no difference between men and women in this matter. There is a difference between them in reciting aloud or whispering though.
In prayers that must be recited aloud for men (the fajr, maghrib and isha prayers), women can recite them silently or aloud, and if a non-mahram can hear their voice, they must recite it silently (obligatory precaution). Please do note that there is a difference between reciting silently and only passing the words through the mind. In the first, there is still recitation, but in the form of whisper, while in the latter, there is no recitation at all, thus making it insufficient for the prayer. On this basis, even moving the lips with absolutely no sound or low whisper will not suffice either.