Based on Shopify documentation for webhooks, it appears you can create a webhook based on create/update events for a fulfillment object.
Based on their API reference for the Fulfillment class, it has attributes such as:
- status
- tracking_company
- tracking_numbers
- tracking_urls
- updated_at
As such, it seems like you should be able to create a webhook for fulfillment update events, and have it POST to an endpoint of your choice. The POST request body will include an instance of the object (XML or JSON payload depending on what you pick when you create the webhook), which will have attributes including the ones mentioned above.