It should be known that while performing Prayer, at least one has to move the lips with the recitation, according to the Maliki School of fiqh. According to the Shafi`i School and other Muslim jurists, while performing Prayer one has to recite with the lowest voice with which one can hear oneself recite.
As for offering the obligatory Prayer while reciting in the mind or heart, one’s Prayer is invalid because recitation is one of the pillars of Prayer, bearing into consideration that reciting or reading indicates moving the lips with the recitation.
Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states: General understanding among scholars is that our tongues, minds, and hearts should all participate in the act of salah. If, however, for some reason a person cannot move his lips, then his salah is valid provided at least his mind and heart are fully participating in the act of salah. But this exception is granted only to those who are prevented from using their tongue or lips, and not to those who have no excuse.
This is as far as salah is concerned, for we are not at liberty to change the format of salah. The Prophet (peace and blessings be upon him) used to repeat the words, “Pray as you have seen me praying.” And what we described above is the method of the Prophet’s Prayer.
Now coming to dhikr in general, however, there is no need to move your lips always; it is perfectly acceptable to make dhikr in your heart or mind without involving your tongue or lips.