Have a look at Managing Hierarchical Data in MySQL. It discusses two approaches for storing and managing hierarchical (tree-like) data in a relational database.
The first approach is the adjacency list model, which is what you essentially describe: having a foreign key that refers to the table itself. While this approach is simple, it can be very inefficient for certain queries, like building the whole tree.
The second approach discussed in the article is the nested set model. This approach is far more efficient and flexible. Refer to the article for detailed explanation and example queries.