The US suit comes just two weeks after Apple faced a similar antitrust hit in the EU.
The tech giant was fined €1.8bn ($1.9bn, £1.5bn) by the European Commission for breaking competition laws over music streaming.
Apple was found to have stopped streaming services like Spotify from informing users of ways to pay outside of Apple’s own app store.
These businesses were frustrated both by this restriction and the fact that Apple took a 30% fee every time someone paid using its own payment system.
Commissioner Margrethe Vestager said Apple had been abusing its dominant position in the market for a decade, and ordered it to remove the restrictions.
She said it had restricted developers from “informing consumers about alternative, cheaper music services available outside of the Apple ecosystem”.
But Apple plans to appeal against the decision, and says there is no evidence that consumers had been harmed.
“The decision was reached despite the Commission’s failure to uncover any credible evidence of consumer harm, and ignores the realities of a market that is thriving, competitive, and growing fast,” it said.