The reader is not really sure what has caused the setting in which McCarthy's story takes place. It is something that resembles post- Apocalyptic reality. Little else is given in terms of detail. In the first chapter, there is description of ash having fallen, with the rivers reflecting some type of fallout that has impaired life from regenerating. The fact that the reader never really knows what happened is something that is fairly deliberate by McCarthy:
... Not knowing all the precise details of the past creates a tension in the story. Readers will find that they want to know more and so will keep turning the pages to learn about the back story...
In this, it is not really given as to whether it was a nuclear catastrophe. Certainly, all signs point to something of that magnitude, but I think it is not the driving point of McCarthy's work, to specifically tell us, the reader, what caused this as much as it is to display the relationship between father and son in an extremely trying setting.