In a blog post, Kaspersky said its app had been in the App Store for nearly three years and Apple had suddenly asked it to remove configuration profiles as this was against the store policy.
But this meant that Kaspersky Safe Kids would no longer have app control and Safari browser blocking, both of which Kaspersky said were essential.
"The first allows parents to specify which apps kids cannot run based on the App Store’s age restrictions," the company said.
The change in policy had come after Apple added a feature to Screen Time that allowed the monitoring of time spent on using certain apps or websites - an app for parental control.
This is not the first time that Kaspersky has gone the anti-trust route.
The company filed a complaint against Microsoft in both Russia in 2016 and Germany in 2017, saying that after Windows 10 was released, Microsoft Microsoft began creating obstacles to the manufacturers of other security solution and devised new methods to force users to forgo third-party software in favour of Windows Defender.
In August 2017, the complaint was resolved after Microsoft agreed to make changes to address these concerns.
Regarding the Apple complaint, Kaspersky said: "From our point of view, Apple appears to be using its position as platform owner and supervisor of the sole channel for delivering apps to users of the platform to dictate terms and prevent other developers from operating on equal terms with it."
It pointed out that music service Spotify and parental control apps AdGuard and Kidslox has also faced blocks by Apple. Spotify had complained to the European Commission about Apple's actions.
"We very much hope that we will also be able to continue our winning relationship with Apple, and that requires us to create an environment where Kaspersky Lab and other companies compete on equal footing," Kaspersky said. "The environment is very different at the moment, which is why we are in the process of applying to the Federal Antimonopoly Service."