Yes, it can be done. This is an
Asclepias incarnata that came up from seed right in the middle of a path leading around the back of our shed. Milkweeds are deep rooted plants, they form a massive tap root that can go down into the earth several feet, usually 6' to 10'.
Early in the year though, you can transplant them. You need to do it right before the green growth takes off though. It really shouldn't be taller than the a few inches. Jam the shovel into the earth a few inches away from the stems and plant it down as far as you can get it. Make your cuts all the way around, and then you're ready to make your move. The trap root will cut, but it should grow back. There are also smaller roots that spread out all around which should sustain the plant while the tap root grows back.
Now doing this removes the drought tolerance of the plant, so you will need to water it regularly, especially over the summer time. Here I've transplanted it right in the garden; it's been growing fine for a week now, but sometimes what can happen is the green growth will die back... so you don't have anyway of knowing if your plant needs watering. This is kind of where problems happen. So it might be best to put in an annual from your local nursery to grow around it just to remind you that this spot needs watering.
Now assuming the new spot is a place where this species can grow, and it had enough of the roots transplanted with it, it should grow back next year happy as ever, and it should be drought tolerant too or at least have enough green growth that you can tell weather it needs watering.
