At the moment it does not look like it is possible to lock down access to the analysis services public endpoint by IP address. It would be good to have a firewall in a similar way to SQL Azure or Azure Data Warehouse.
Mehmet Bakkaloglu commented
Indeed there needs to be a tick box to allow all Azure services through the firewall -- similar to Azure SQL Server
Nick McDermaid commented
It does have a firewall now, but it doesn't automatically support other Azure services, i.e. if I try and process a model from Azure Automation, I need to open the firewall for its Azure IP address.
Måns Barklund commented
This has actually been implemented in Sep 2017: https://azure.microsoft.com/en-us/blog/azure-analysis-services-adds-firewall-support/
JUAN PABLO HORST commented
These services are for business and could managed confidential and important information. There should be a possibility to stablish secure connection to it (VPN) and restrict public access (although user authentication).
Microsoft should be aware of it.