Currently I have a Heroku server running some Node.js code. I use this server as a webhook to receive a POST request from API.AI (Dialogflow) information.
Before starting to research and all the funcionability of Amazon S3, I wanted to see if is possible migrate this Heroku server to Amazon S3 and maintain the API.AI webhook functionality.
No, this isn't possible.
Amazon S3 is an object storage service. It can be used to host static websites, but not websites that require any server-side logic. (Amazon does offer other services that can run Node.js code, like EC2.)