Not sure their is any "written in stone" age when a child is ready to take on music instruction but there are a few important questioning factors to consider in your decision for this.
Some areas to take into consideration would be :
Does your child have the necessary refined motor skills and coordination? Have they yet worked with their hands in crafts or have they learned to ride a bike ? etc.
Do they possess the necessary maturity and attention span that is required? Although most good teachers will keep your child's interest during the course of taking a lesson, your child will at some point need to play/perform what their trying to learn and not be constantly distracted. An attention span of about 15-20min is usually required, as lessons for children just beginning is normally about 30 min. 15-20 for instruction with about 10min of speaking ;motivating and support to hold their interest.
Are your child's fingers developed enough to play the instrument of choice? If say when trying to learn a stringed instrument like guitar or violin, does your child possess the strength to press down on the strings to play a note? If not, it might be wise to wait a little bit .
Have they shown interest about being involved an wanting to play an instrument? Hopefully it's from both the Parent and the child.
Reading comes into play as there will eventually be musical notes to learn and read ; understand and play.
Most all children need your support when taking on a learning process.
This is a very important part of being 'involved' with their learning for them to be successful.
Practice time with learning-doesn't have to be very long but enough to help them 'grasp' and progress in what they're trying to learn, and that's usually where the support comes in from you, the Parent.
Of course there is motivation (usually needed in the beginning), which they depend on you to provide and of course you are the only one who knows when practice time can be scheduled. Usually a routined approach having them practice at the same convenient time each day is the best but with families, sometimes this routine has to be 'worked around'.
Normally once a child gets into a routine and begins to see some progress and has your support, they will enjoy this much more and want to continue not just because their progressing but because it makes them feel good and with many, boosts their self esteem.
These are just a few points to consider and hope in some way this helps in your decision. To me there is not too many more wonderful things in life than to see our children happy ; motivated and learning new skills.... and especially the skill of learning how to play their favorite musical instruments!