You might want to poke a small hole in the middle of that stain to allow any accumulated water out if it is still pooling there. If the drywall doesn't buckle, you can probably put a stain blocking primer on it and repaint. If you do poke a hole, you want to have a bucket to catch anything that comes out.
It would be better to open up a bigger hole to let it air out and dry. I'd make the hole big enough to put a fan directed there. Dark, damp things can grow some nasty stuff. As long as it can dry out fairly soon, you probably haven't done any structural damage other than on the drywall, and that can take some wetting, but not much.
I take it that the sink doesn't have an overflow? Might be something to consider in the next remodel! If it does have an overflow, clean it out so it doesn't happen again.