بسم الله الرحمن الرحيم
Shaikh bin Baz رحمه الله was asked the following question: “Is it permissible to hold the mus’haf with the left hand?”
He replied, “I am not aware of anything regards to this, even though of course holding it with the right hand is better, the right is better generally, the prophet صلى الله عليه و سلم would use his right hand for arranging his hair, giving and taking, shaking hands etc; as for the left then it is for other than that [i.e. cleaning oneself after answering the call of nature etc].
If though there was a need to hold the mus’haf with the left hand [whilst reciting or otherwise] due to the right hand becoming tired, or due to a need whereby the right hand was required to pick something up or do something, or something similar to such needs, then there is no harm in holding the mus’haf in the left inshaa’ Allah. So whether he placed it in the left or right and read would be ok, however no doubt the right is better and superior as the prophet صلى الله عليه و سلم would use the right for the good affairs”.
[Based on a Fatwa from Shaikh bin Baz’s Official Website]