Hit it with a rock. A big rock.
Something like Ceres might do, if you could somehow get it into an orbit that hits the moon with sufficient relative velocity. Alas, moving Ceres significantly from its current orbit is likely itself a non-trivial task.
A stray Kuiper belt object might be more practical, if only because there are more sufficiently large bodies out there, and also because the long fall from the Kuiper belt to the inner system would naturally give the impactor a highly eccentric orbit that could intersect the Moon at a sharp angle and high velocity difference.
You'd still have the problem of getting the object to the inner system in the first place, but I could buy a scenario where a collision (or a near-miss) with another KBO sends the would-be impactor on an unstable orbit leading to an eventual close encounter with Neptune, which, with some good (or bad, depending on how you look at it) luck, might send it towards the inner system and an eventual collision with the Moon.
Of course, you could go further afield and have the object come in from the Oort cloud, or even from interstellar space. Most solar system formation models predict a large number of small planetesimals getting scattered out of the system when it forms, so it stands to reason that there must be a sizeable population of stray planets out there in interstellar space, and that they'll occasionally make a near pass to a star such as the Sun.
Of course, such encounters are (fortunately) not that common, and most such bodies will just pass through the solar system without hitting anything anyway, but having one fall in and hit the Moon is still perfectly within the realm of possibility. As a bonus, a stray planetesimal could potentially fall in from any direction, even well away from the plane of the ecliptic, which could let you get some quite interesting orbital changes when it hits.
In any case, a body smaller than the Moon, passing the Earth at the Moon's distance, isn't going to directly disrupt the Earth to any significant extent (unless you count making a lot of astronomers soil their underwear when they first spot it). Any tidal effects will, by definition, be smaller or comparable to the lunar and solar tides the Earth already experiences, and any gravitational effects on the Earth's orbit should be negligible.
The bad news, however, is that anything massive hitting the Moon at high speed is going to scatter off lots of smaller rocks when it hits, some of which will likely hit the Earth. So Earth as a whole might be fine, but you'd likely be looking at some rather big meteor impacts as secondary effects, potentially disrupting the biosphere and any civilization down here. Worse yet, since the scattering from the lunar impact is likely to be rather chaotic and unpredictable, we won't be able to easily predict how many secondary impacts might hit the Earth, or when and where they would hit.