The firms prevented players from installing one of the world's most popular games from their platforms in a row over payment methods.
Fortnite is free, but users can pay for in-game additional items like weapons and skins.
However, earlier on Thursday the game’s developer, Epic Games, introduced a direct payment plan that bypassed Apple and Google's technologies.
Both companies then removed the game, saying Epic's new system violated their in-app payment guidelines.
The developer responded by taking the issue to the US courts.
Epic is not demanding any money from Apple or Google but rather injunctions that would end many of the companies' practices related to their app stores.
Launching its lawsuit, the developer said: "Apple has become what it once railed against: the behemoth seeking to control markets, block competition, and stifle innovation. Apple is bigger, more powerful, more entrenched, and more pernicious than the monopolists of yesteryear."
Epic also attacked Apple on social media, launching a campaign with the hashtag #FreeFortnite, urging players to seek refunds from Apple if they lose access to the game, and creating a parody of Apple's famous "1984" television ad.
In the parody, which quickly garnered hundreds of thousands of views, a female Fortnite fighter hurls a unicorn-shaped club to smash a screen on which an Apple-headed character speaks of "the anniversary of the platform unification directives."
Epic Games has defied the App Store Monopoly. In retaliation, Apple is blocking Fortnite from a billion devices.
Visit https://t.co/K3S07w5uEk and join the fight to stop 2020 from becoming "1984" https://t.co/tpsiCW4gqK— Fortnite (@FortniteGame)August 13, 2020
Apple typically takes a cut of between 15 and 30 per cent for most app subscriptions and payments made via apps.
Analysts believe games are the biggest contributor to spending inside the App Store.
In a statement, Apple said Fortnite had been removed because Epic had launched the payment feature with the "express intent of violating the App Store guidelines" after having had apps in the store for a decade.
"The fact that their (Epic) business interests now lead them to push for a special arrangement does not change the fact that these guidelines create a level playing field for all developers and make the store safe for all users," Apple said in a statement.
Google also removed "Fortnite" from its Play Store, but did not immediately respond to a request for comment on the lawsuit.
"However, we welcome the opportunity to continue our discussions with Epic and bring Fortnite back to Google Play," Google spokesman Dan Jackson said in a statement.
Mr Jackson said Epic had violated a rule requiring developers to use Google's in-app billing system for products within video games.
Fortnite's removal from the App Store means that new players will not be able to download it, but the game should continue to work on devices where it is already installed.
Epic Games does not disclose how many Apple iOS users Fornite has.
Many fans play the game primarily on PCs or gaming consoles while using their mobile phones as a backup, but iPhone users generate far more revenue for Epic.
In both Apple's App Store and Google's Play Store, Fortnite had about 2 million downloads in July 2020, according to mobile analytics firm SensorTower.
Fortnite is currently unavailable on Google Play. More information will be forthcoming soon.— Fortnite (@FortniteGame)August 14, 2020
Because Android functions differently from iOS, users can still download Fortnite from Epic's website and other non-Google stores and install it on their devices, Epic said in a blog post earlier on Thursday.
"Epic is not seeking any monetary relief, but rather only an order enjoining Google from continuing to impose its anti-competitive conduct on the Android ecosystem," it said in its lawsuit.
In a statement, Spotify Technology SA, a streaming music rival to Apple that has filed an antitrust complaint against the iPhone maker in Europe, applauded Epic's move.
"Apple's unfair practices have disadvantaged competitors and deprived consumers for far too long," Spotify said.