In your implementation you could close it your self, if when the iteratoror is exhausted.

public boolean hasNext() {
       .... 
       if( !hasNext ) {
           this.close();
       }
       return hasNext;
 }

And clearly document:

This iterator will invoke close() when hasNext() return false, if you need to dispose the iterator before make sure you call close your self

example:

void testIt() {
     Iterator i = DbIterator.connect("db.config.info.here");
     try {
          while( i.hasNext() {
              process( i.next() );
          }
      } finally {
          if( i != null )  {
              i.close();
          }
      }
  }

Btw, you could while you're there you could implement Iterable and use the enhanced for loop.