Can I assign a reserved IP to Azure Container Instances (ACI)?
UPDATE
You can now assign a private IP address by joining your container group to a VNET! Check out details at https://aka.ms/aci/vnet.
You cannot assign a private IP address to a container group today. We are enabling assignment of private IP addresses to container groups later this year so you can join a container group to a new or existing private VNET.
Note ACI also does not guarantee a static IP address for a container group, the link provided by Joey details how to setup a DNS name label to utilize a reliable endpoint though.
Hope this helps!