This happens to me sometimes after I run (not usually with cycling though). Is it soreness or tightness? If it's tightness try taking a soup can (someone else mentioned a golf ball but a soup can worked better for me) and place it under your foot. Put some weight on it and roll it from the balls of your feet to the heel a few times. It will stretch the muscles in the sole of the foot and that should help.
If it's soreness, it could be caused by any number of things and you should speak to a pediatrist as many have already mentioned.
Just something else to think about - do you have flat feet / do your toes cramp? I would guess not because pain caused by flat feet is usually on the top of the foot but it could be linked.