In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner, thanks for your question. We implore Allah to guide our children to the best and to guide us all to that which pleases Him, Amen.
It is well known that fasting, like other obligatory acts of worship, becomes mandatory when the person reaches the age of puberty. As regards children, we would like to stress that it is highly desirable to encourage them to fast when they reach the age of seven if they are physically capable of doing so.
Here, the prominent Saudi Islamic lecturer and author, Sheikh Muhammad Saleh Al-Munajjid, states the following:
It is encouraged that children observe fasting when they reach the age of seven, if they are physically capable of bearing it.
Some Muslim scholars state that the child should be physically disciplined if he does not fast by the age of 10, which is the same rule that is applied to prayer. This is stated in the book of Al-Mughni. Al-Rubayyi’ bint Mu’awwadh (may Allah be pleased with her) said about fasting `Ashoura’ at the time when it was mandatory to fast it and not voluntary: We used to make our young children fast, and we made them a toy made out of wool. If one of the them cried (wanting) food, we would give him the toy to distract him until it was time to break the fast. (Reported by Al-Bukhari ). (`Ashoura’ is the tenth day of the month of Muharram. Although fasting this day is now voluntary, the majority of Muslims usually fast it.)
Some people are quite lenient and lax when it comes to making their children fast. A situation may even arise where the young child feels enthusiastic and chooses to fast and is physically capable of doing so, then his father or mother order him to break his fast claiming that it is out of sympathy. Little do they know that real sympathy is in stressing the importance of fasting and teaching the child about it. Allah Almighty says, (O you who believe! Ward yourselves and your families off from a fire (Hell) whose fuel is of men and stones, over which are appointed angels stern and severe, who do not disobey the commands they receive from Allah, and execute that which they are commanded.) (At-Tahrim 66:6)
Also, we must pay extra attention to the young girl when she first starts fasting after she reaches puberty. There is a possibility that she will fast while she has her period (the first time) out of shame or shyness, and end up not making up the days later on.
Excerpted with modifications from http://www.islam-qa.com
Moreover, Dr. Muzammil Siddiqi, former president of the Islamic Society of North America, adds:
Fasting, like all the other obligations in Islam, becomes mandatory at bulugh. That is when a person reaches the age of puberty. There is a Hadith of the Prophet (peace and blessings be upon him) in which he said, “Tell your children to pray when they are seven years old and discipline them if they don’t when they are ten years old.”
The same can be said about fasting. That is, we should encourage our children to fast when they are seven years old and we should emphasize fasting to them when they are ten, but it becomes obligatory when they reach the age of puberty.