How to lose the moon? In this worldbuilding question, the moon is gone:


  an extra-solar gas giant passed close by Earth in which the Moon was
  knocked from orbit to become a planet in an independent orbit, as well
  as sending Mercury crashing into its parent star.


So by introducing a rogue planetoid, the orbit of both the Moon and Mercury needs to be affected, with at least the former surviving the encounter.

Is this possible? If so, what are the requirements (mass, velocity, proximity)?  Would it be possible for it to happen and affect the Earth minimally, so that it remains habital?
The Earth and moon orbit around a barycentre that is "about 3/4 the radius of Earth" away from the Earth's centre: https://en.wikipedia.org/wiki/Orbit_of_the_Moon. Removing the moon would almost certainly affect the Earth's orbit around the sun due to the change in the centre of mass, and probably a resultant change in momentum of the Earth system (such as it was). That's without even considering the gravitational tug of the planetoid on the Earth, and that of the moon as it gets snatched away. I would think it spectacularly unlikely for the interaction to leave Earth travelling along the orbit of the centre of mass of the old Earth-moon system. But, I haven't actually modelled it, so I might be wrong there.