Combine coconut milk, lime juice, wine, curry paste, garlic, fish sauce, and sugar in a 6- to 8-quart wide pot and bring to a boil over high heat.
Cover and boil, stirring occasionally, for 2 minutes.
Add mussels and toss to combine.
Cover pot and cook, stirring occasionally, until mussels just open wide, about 6 minutes.
Discard any unopened mussels. Just before serving, toss mussels with cilantro. Serve with lime wedges.