Not sure why you want to restrict access to the site to only traffic coming from the Application Gateway because if you configure it and add the website in the backend of Application Gateway. The traffic from a client will always reach the website through the Application gateway as the Application Gateway works as an application proxy by accepting traffic and based on rules that are defined with it, routes the traffic to the appropriate back-end instances.
You may want to know to restrict access on the application gateway subnet via NSG. Then the inbound or outbound traffic in the Application Gateway subnet will be filtered via NSG.
Network Security Groups (NSGs) are supported on the application
gateway subnet with the following restrictions:
Exceptions must be put in for incoming traffic on ports 65503-65534
for the Application Gateway v1 SKU and ports 65200 - 65535 for the v2
SKU. This port-range is required for Azure infrastructure
communication. They are protected (locked down) by Azure certificates.
Without proper certificates, external entities, including the
customers of those gateways, will not be able to initiate any changes
on those endpoints.
Outbound internet connectivity can't be blocked.
Traffic from the AzureLoadBalancer tag must be allowed.
Hope this will help, let me know if you have any other concerns.
Update
If you just want to whitelist the Azure service on the firewall, you can read the Azure Datacenter IP Ranges. You can figure out which datacenters your service are located in then narrow down the IP ranges.
