In ECS documentation it says you can scale to zero:

If you want your task count to scale to zero when there’s no work to be done, set a minimum capacity of 0. With target tracking scaling policies, when actual capacity is 0 and the metric indicates that there is workload demand, Service Auto Scaling waits for one data point to be sent before scaling out. In this case, it scales out by the minimum possible amount as a starting point and then resumes scaling based on the actual running task count.

https://docs.aws.amazon.com/AmazonECS/latest/developerguide/service-auto-scaling.html

However, when I tried to run a basic nginx web server, there will always be at least 1 service running.

Am I doing something wrong, or is this not possible.