You can do this by creating a factory method in MyObject:
class MyObject {
public static MyObject create() {
return new MyObject();
}
}
then mock that with PowerMock.
However, by mocking the methods of a local scope object, you are depending on that part of the implementation of the method staying the same. So you lose the ability to refactor that part of the method without breaking the test. In addition, if you are stubbing return values in the mock, then your unit test may pass, but the method may behave unexpectedly when using the real object.
In sum, you should probably not try to do this. Rather, letting the test drive your code (aka TDD), you would arrive at a solution like:
void method1(MyObject obj1) {
obj1.method1();
}
passing in the dependency, which you can easily mock for the unit test.