The app, which charged $80 per year, provided notifications every time a targeted user liked or commented on another Instagram user's photo, as well as details about the gender of that user.
Like Patrol creator Sergio Quintero accused Facebook-owned Instagram of double standards when it comes to user privacy and vowed to appeal Apple's decision. He also revealed plans to release a web and Android version of the app.
"There is a strong hypocrisy in Facebook's condemnation of our app," Mr Quintero told The Independent. "Like Patrol does not collect data from Instagram users, it provides the users with a tool to rearrange information that is already available to them."
A spokesperson for Instagram said that data "scraping" violated its policies, adding: "Like Patrol was scraping people's data so we are taking appropriate enforcement action against them."
While the app could be used by anyone, Like Patrol primarily aims its service at people in relationships. When it first appeared in Apple's App Store earlier this year, tech publication CNet labelled it a "stalking app" due to the functionality it provided.
Like Patrol boasts on its website of allowing people to keep tabs on their partner through "Instagram activity insights" relating to the target's social media activity.
It states: "New guy? New girl? What are they up to on Instagram? With Like Patrol you can see the posts they specifically like!"
A similar version of this tool used to be available through Instagram's official Following Tab, however this feature was discontinued in October.
"If our app's functionality did violate any [of Apple's] policies, then Instagram would have violated the exact same policies between 2011 and 2019 with the Following Tab. Why weren't they taken down?" Mr Quintero said.
"We have decided to make Like Patrol open source and allow anyone to use it. We will be announcing the release in the coming days."
Apple did not comment on the app but confirmed that it had been removed for violating its guidelines.