Shaykh Ibn Uthaymeen was asked:
I see many people who read the Qur’an, especially in the circles of the Qur’an, shaking or moving with a movement. What is the ruling on this shaking?
“If this comes automatically, then there is no harm in this because some people find it helpful to shake when reciting. If it comes as a form of worship, then it is not allowed. It is an innovation. With that, we speak to those who shake automatically to look within themselves and leave off shaking. This is because others may take them as an example and think that this is a legislated affair”. End translation. [Reference]
Faisal Ibn Abdul Qaadir Ibn Hassan