This depends on where you are giving bath to your child, is it a toilet come bathroom or just a bathroom. If it is just a bathroom, then it is permissible to recite Quran while giving your child his bath. But if there is a toilet along with bathroom, then it is haraam to recite Quran in there, whether it is done in a low voice or a loud voice, because the Qur’an is the word of Allah and it should be respected and honoured.
Shaykh Ibn Baaz (Rahimuhullah) was asked: What is the ruling on reciting Qur’an in the bathroom?
He replied: It is not permissible to recite Qur’an in the bathroom, because that is a place for relieving oneself. As for places for doing wudoo’, there is nothing wrong with reciting Qur’an there, but in places where one relieves oneself – the toilet – it is not permissible.
[End quote from Majmoo‘ al-Fataawa, 29/31]
But if you are giving your baby his bath in a place where one does not go to relieve oneself, then there is nothing wrong with reciting Qur’an while giving him his bath, even if that is while removing impurities (najaasah), because there is nothing to indicate that it is not allowed. But it is better not to recite Qur’an in that situation, because what is required of the one who recites Qur’an is that he should recite it with deliberation and pondering the meaning, which is the greater purpose behind reciting Qur’an.
An-Nawawi (Rahimuhullah) said: When a person starts to recite Qur’an, he should be in a humble frame of mind, focusing on and pondering the meaning. This is what is required and is the purpose of it; in this way minds are put at rest and hearts are illuminated. Allah, may He be exalted, says:
“(This is) a Book (the Qur’aan) which We have sent down to you, full of blessings, that they may ponder over its Verses” [Saad 38:29]
“Do they not then consider the Qur’aan carefully?” [an-Nisa’ 4:82].
And there are many hadeeths which speak of that.
[End quote from Sharh al-Muhadhdhab, 2/190]
He (Rahimuhullah) also said: It is not makrooh to recite Qur’an when walking in the street, so long as one is not distracted [End quote from Sharh al-Muhadhdhab, 2/189]
Shaykh Ibn ‘Uthaymeen (Rahimuhullah) said: The purpose behind reciting Qur’an is, as well as it being an act of worship, to understand its meanings so that one will be better able to act upon it. It is for this purpose that this blessed Qur’an was revealed. Allah, may He be exalted, says: “(This is) a Book (the Qur’aan) which We have sent down to you, full of blessings, that they may ponder over its Verses, and that men of understanding may remember” [Saad 38:29].
As that is the case, the one who reads or recites Qur’an should focus properly on what he is reading or reciting, and he should ponder its meanings and not let his heart or physical faculties be distracted by anything else, such as housework or other activities. As Allah has commanded the one who hears the Qur’an to listen to it and be silent so that he can focus and ponder the meanings of what he is hearing, then this applies even more to the one who reads or recites it.
[End quote from Fataawa Noor ‘ala ad-Darb]