To a large pot, add the coconut milk and 4 cups water. Heat to a boil on high. Whisk in the red curry paste until dissolved.
In batches, stir in the spinach, until just wilted. Remove the ramen noodles from the packets, discarding 2 flavor packets. Heat liquid to a simmer and add noodles and 1 flavor packet. Cook 3–5 min., until just al dente.
Divide noodles and soup among 4 serving bowls. Tear the cilantro and sprinkle over noodles.