The legal complaint revolves around iOS 8 and the amount of memory it reserves for itself on iPods, iPhones and iPads.
The complaint alleges that it takes up so much space that far less than advertised is left for people to store their own data.
Apple has yet to issue any official comment on the lawsuit.
The complaint has been filed in California by Miami residents Paul Orshan and Christopher Endara who say that iOS 8 can occupy up to 23.1% of the memory available on some Apple devices.
In addition, upgrading devices from the earlier iOS 7 to 8 can cause people to lose up to 1.3 gigabytes of memory, said papers filed in support of the legal action.
The amount of memory taken up by iOS 8 can mean users run out of storage and, Paul Orshan and Christopher Endara allege, this is helping Apple force people to sign up for its fee-based iCloud storage system.
The lawsuit is seeking millions of dollars in damages for those using Apple devices facing the storage squeeze.
So far, Apple has not responded to requests for comment on the lawsuit.
The latest upgrade to iOS 8 was released in late September but Apple was forced to withdraw and then re-issue it because the first version meant a lot of iPhone 6 and Plus handsets could no longer make calls.
Apple issued a public apology over the botched update but said only 40,000 people were affected by it.
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