This depends on each individual child and teacher. I believe a child's music education should start at birth in some senses, and you can read about that in my "Preparing a young child for music lessons" post. But when it comes to more formal lessons, I would recommend one of many pre-school programs. My first year of teaching cello lessons, my youngest students were 6 years old, and two of them had participated in pre-school programs. Both had what many would believe was a "natural talent" for music.
Some start Suzuki and other lessons very early, but I would like my students to be about four years old [Edit: Now that I have had my Suzuki training, I would possibly start a three year old], depending on the child. They need to be ready to sit still and listen for 10 - 15 minutes at a time. It is my experience that starting before age 11 is best. Obviously a child who is 11 will learn at a faster rate than a three or four year old, but there are still benefits to starting younger. A younger child is much more eager to copy and please his parents and so is more easily motivated. A younger child usually has more time to devote to music. They also reap the many benefits of brain development which studying music provides. (See my website.) And hey, learning music is FUN! An older child might feel more pressured to "catch up" in their skills, where a younger child's practice can be more relaxed. If you would like your child to learn with me and they are younger than four, I still would recommend looking into some of the other pre-school programs in our area.
Children learning music so young do depend heavily on parents' participation for success, attending lessons and helping with practice at home, so take that into consideration, too, when deciding when to start your child's lessons. But consider the benefits of this one-on-one time with your child, too! This can be a very precious time between child and parent.
Whichever music lessons you take your child to, start looking maybe a year before you would like them to start. You can then spend some time visiting and observing the teacher(s) to see how they deal with children, what the atmosphere is like, what is expected of the children. Also, the teacher may have some ideas of things you can do at home to prepare your child. The teacher also may have a wait list. (At this time I have ONE spot open!) The child may be motivated, too, by watching other children playing an instrument or other music games a bit before they begin themselves.
And if you've already missed the under 11 window? Well, it's never too late to learn, but it does get more difficult! :-)