Yes, you can put shutters on an arched window! And… shutters for arch shaped windows make perfect sense because they can be opened to allow in additional light or closed to less light and extra privacy. Firstly, traditionally shaped half round window are no longer an impediment to beautiful custom shutters. This type of plantation shutters are a popular and subtle window fashion for a good reason. … Just because they are old, that does not mean shutters are out of fashion. The style or design may be the same, but the functionality makes them a worthy choice.