The suit follows the U.S. Federal Trade Commission's lawsuit against Qualcomm earlier this week over unfair patent licensing practices.
Shares of Qualcomm, which had been up 1 percent earlier in the day, were were down nearly 2.5 percent by the closing bell.
Apple says that Qualcomm has taken "radical steps," including "withholding nearly $1 billion in payments from Apple as retaliation for responding truthfully to law enforcement agencies investigating them."
Apple added, "Despite being just one of over a dozen companies who contributed to basic cellular standards, Qualcomm insists on charging Apple at least five times more in payments than all the other cellular patent licensors we have agreements with combined."
Apple also alleges that once it began cooperating with Korean authorities' antitrust investigation of Qualcomm, the company withheld $1 billion in retaliation. Korean regulators fined Qualcomm $854 million for unfair trade practices in December.
Apple shares were little changed.
Here's the full Apple statement:
"For many years Qualcomm has unfairly insisted on charging royalties for technologies they have nothing to do with. The more Apple innovates with unique features such as TouchID, advanced displays, and cameras, to name just a few, the more money Qualcomm collects for no reason and the more expensive it becomes for Apple to fund these innovations. Qualcomm built its business on older, legacy, standards but reinforces its dominance through exclusionary tactics and excessive royalties. Despite being just one of over a dozen companies who contributed to basic cellular standards, Qualcomm insists on charging Apple at least five times more in payments than all the other cellular patent licensors we have agreements with combined.
To protect this business scheme Qualcomm has taken increasingly radical steps, most recently withholding nearly $1B in payments from Apple as retaliation for responding truthfully to law enforcement agencies investigating them.
Apple believes deeply in innovation and we have always been willing to pay fair and reasonable rates for patents we use. We are extremely disappointed in the way Qualcomm is conducting its business with us and unfortunately after years of disagreement over what constitutes a fair and reasonable royalty we have no choice left but to turn to the courts."
In a statement, Qualcomm said that while the company was still in the process of reviewing the complaint in detail, it felt that Apple's claims were "baseless."
"Apple has intentionally mischaracterized our agreements and negotiations, as well as the enormity and value of the technology we have invented, contributed and shared with all mobile device makers through our licensing program," Qualcomm Executive Vice President and General Counsel Don Rosenberg said in the statement.
"We welcome the opportunity to have these meritless claims heard in court where we will be entitled to full discovery of Apple's practices and a robust examination of the merits."
— CNBC's Josh Liption and Megan Hawkins contributed to this report.