Function Apps that run on a Dynamic service plan are restricted in certain ways (as expected).
Is it possible somehow to call an on-premises resource (via a VPN or Hybrid Connection) from a Function App in a Dynamic service plan?
Would you be able to consider using the Azure Service Bus? Functions have support for adding messages to the servicebus queue (read more: https://azure.microsoft.com/en-us/documentation/articles/functions-bindings-service-bus/) and then in your on-prem environment you'd process the servicebus queue.
This is what I've done with provisioning logic for Web Jobs and other cloud-to-onprem environments previously, while I've yet to try it with Functions - but as per the article mentioned Functions should be able to process the messages to the SB queue.
Hope it helps.