A wood chair made for indoor use may withstand a little moisture, but it isn't designed to be left out in the rain, even if it has a protective finish. Remove the visible water with towels; then air dry the chair as soon as possible to help prevent the wood from swelling and rotting. This also helps prevent damage to the finish.
The Drying Process
Pat the chair dry with absorbent white towels to remove as much moisture as possible; dyed fabrics may bleed onto the wood. Keep blotting the chair until no more moisture transfers to the towels. Wipe off any hardware such as screws or nuts visible anywhere on the chair, including the bottom, in case water splashed on them. Keep the chair in a protected outdoor environment, such as a covered porch or garage, or indoors if the humidity and temperature matches outdoor conditions. Drastic changes in humidity or temperature may cause the chair to crack, buckle or swell, so it is best to allow it to dry out slowly. Turn on a portable fan, blowing near but not on the chair, to help it dry for at least several hours. Take the chair indoors, but do not use it for a while; it may take weeks for the chair to dry out completely if the rain soaked the wood, such as in the space between joints.