You can’t do this with Mockito, but Apache Commons actually has a way to do this using one of its built in utilities. You can put this in a function in JUnit that is run after Mockito injects the rest of the mocks but before your test cases run, like this:
@InjectMocks
MyClass myClass;
@Before
public void before() throws Exception {
FieldUtils.writeField(myClass, "fieldName", fieldValue, true);
}