It depends. Every child develops differently and every piano teacher has their preferences. I, personally, will not start a child on private piano lessons until they have:
Developed fine motor ability in their hands and fingers
Can sustain concentration at the piano bench for at least 15 minutes at a time
Can listen to and follow instructions well
Can count to 10
Can read all 26 letters of the alphabet
Can verbally communicate with me in complete sentence
Shows an interest in music making
For some children, all of these skills may be in place as early as 3 years old and for others, it may not happen until they are 8 years old. If you're not sure if your child is ready, get in touch with me. If there is a spot in my studio for a potential young student, I will assess your child's readiness at the trial lesson.