In preview – Virtual network service endpoints for Azure database services for MySQL and PostgreSQL

 Virtual network service endpoints for Azure database services for MySQL and PostgreSQL are available in preview in all accessible regions. Virtual network service endpoints allow you to isolate connectivity to your logical server from only a given subnet or set of subnets within your virtual network. Traffic to Azure database services for MySQL or PostgreSQL from the virtual network service endpoints stays within the Azure backbone network. This direct route will be preferred over any specific routes that take internet traffic through virtual appliances or on-premises.

Learn more about services for MySQL.

Learn more about services for PostgreSQL.

Source: Azure Roadmap