Run docker container on azure
But it is really easy.. once you know where to find the docs :-). I would take the azure docs as a starting point as there are multiple options when it comes to hosting containers in Azure:
If you're looking for this...
Simplify the deployment, management, and operations of Kubernetes -> Azure Container Service (AKS)
Easily run containers on Azure with a single command -> Container Instances
Store and manage container images across all types of Azure deployments -> Container Registry
Develop microservices and orchestrate containers on Windows or Linux -> Service Fabric
Deploy web applications on Linux using containers -> App Service
Based on your info I would suggest storing the image using the Azure Container Registry and host the container using Azure Container Instances. No need for a VM to manage this way.
There is an excellent tutorial you could follow (I skipped the first 1 step since it involves creating a docker image, you already have one)
Another complete guide of pushing your image to azure and create a running container can be found here.
The good thing about Azure Container Instances is that you only pay for what you actually use. The Azure Container Registry is a private image repository hosted in Azure, if course you could also use Docker Hub but using ACR makes it all really simple.