You can now use the Azure CDN to access blobs with custom domains over HTTPS. See the following article for instructions on how to do so: https://docs.microsoft.com/en-us/azure/storage/storage-https-custom-domain-cdn. Having talked to a number of customers, we concluded that this solution addresses many scenarios where the need for HTTPS access to blobs with custom domains exists.
Native Azure Storage support for using SSL to access blobs at custom domains is still on our backlog. We would love to hear about your scenarios where using the Azure CDN is not an acceptable solution, either by posting on this thread or sending us an email at email@example.com.Anonymous commented
The idea was shared on July 18, 2012. It is 2017 and this is still not available. Shame (ring) shame (ring)