Most interceptor systems are designed to hit missiles in the middle of their flight plan. For the US, that means over the Atlantic or Pacific ocean. So the warhead(s) likely break up and their radioactive materials are dumped into those oceans and the atmosphere above them, either in mostly intact chunks of debris, or in the form of dust when they burn up. If they did detonate (unlikely but not impossible) it would be well away from populated areas...

Bare in mind that no one has actually managed to intercept