Notes on weed cultivation: First off, congratulations on your milkweed being covered with caterpillars. I have had mine for at least 5 years now, and no caterpillars (well a few that happened to show up in Nov. a couple times, but they didn't survive Dec.)
I'm kind of surprised that the one plant is your only one, since I've got it now springing up all over the yard, what with the wind and all those million little parachute-seeds from each seed pod.
I did a little experiment with a milkweed plant yesterday. I dug it out by the root. A simple naked little scraggly sweet-potatoey looking knot with almost no root hairs or clinging dirt. Then I re-planted it a few feet away from where it came from, trying to see how hardy these weeds are. An hour later it was bent and wilty, its little leaves hanging limp off the stem. Well, no wonder, its root was sitting in dry dust, so I took pity & watered it(!) This morning it was perky and fresh, looking like nothing was bothering it. (not even the impending arrival of Monarchs). I think it's going to be just fine.
So I advise first trying JStorage's answer, and if that nasty old grass (or whatever it is) persists, don't fear destroying the delicate milkweed by digging up the whole clump, clearing out the interloper by the roots, & replanting the weed.
I hope those Monarchs appreciate it.