A few weeks of not participating in a specific activity seems like a small sacrifice to adults. To kids it can seem like the end of the world. As parents it is our job to make the unpopular decisions and make sure the injury is properly cared for.
Involve the child in all of the information about the injury and explain all of the ramifications of each decision. Next month is a long way off to a child, but as adults we know how insignificant that amount of time will be in the long run.
Support, encourage and love your athlete!