There is no built-in way to password protect an individual folder within a blob storage account. However, there are several options to accomplish what you are looking for.
- If you use Azure Active Directory roles and don't have a lot of folders that need to be password protected, it may be easier to create separate Blob storage accounts for each "folder", and then use the built in access controls in Azure.
- Create a simple proxy service to access blob storage. In this service, capture the uploaded contents and zip them with a password, then store the zipped file. For downloading, in the proxy service you can then check the password on the zip file and if it is valid, then download the full content. Here is a related example: https://github.com/icsharpcode/SharpZipLib/issues/303
- Create an authenticated proxy service that keeps track of the folders and passwords and again manage access via this proxy service. This is likely the most work out of the three options and likely take the most time to make secure.