Like Patrol - which launched in July - was described by its founder Sergio Luis Quintero as "the defunct 'Following' Tab, on steroids", and the social media platform itself tried to force the app to shut down last month over concerns it was scraping people's data without their consent.
Now, Apple has removed the programme from its App Store.
However, Quintero told the BBC: "We plan to appeal this decision in the coming days."
He has also revealed his intention to make Like Patrol's code 'open source' to allow other people to reproduce its functionality.
The app hasn't appeared on Google Play.
Last month, Instagram - which is owned by Facebook - issued a cease and desist letter as it sought to shut down the app.
In a statement, the company previously said: "Scraping violates our policies, and we take action against companies who we find to be engaging in it.
"Like Patrol was scraping people's data, so we are taking appropriate enforcement action against them."
Instagram's 'Following' tab allowed users to see whose posts their friends like, and what comments they left on other feeds.
Meanwhile, Like Patrol had promised to send notifications anytime a follower likes a post or comments, and this information is then broken down by gender along with a list of who a person interacts most with.
On its website, the company said: "New guy? New girl? What are they up to on Instagram?"