Be aware, all files with this change cannot be read at all, meaning a text file in the folder, or a configuration file, will not be able to opened or edited. With the former method, the affected users will not be able to read the files or folders contents, thereby making it unable to be executed. Alternatively, you can remove the execute permission in the advanced permissions of the aforementioned dialog. You can either remove a user or group's read access to a folder and/or files in the File Permissions dialog.
There are three methods I can think of off the top of my head on how this can be done, all permissions related.