The SEC is examining potential violations of federal securities laws related to Iconix's acquisition of intangible assets associated with Jay-Z's Rocawear apparel brand, according to the SEC's statement about the subpoena.
Carter had no role in Iconix's actions as a public company, a spokesperson for the superstar said in a statement.
In March 2016, Iconix publicly announced a $169 million write down of Rocawear, and in March of this year, Iconix announced a further write down of $34 million.
Among other things, the SEC said it wants Jay-Z to reveal the value of the Rocawear trademark and his involvement with the brand after the sale to Iconix.
The SEC initially sent a subpoena to Carter in November, and then another one in February, but he did not comply with either one.
As stated in the SEC's application, a subpoena enforcement action is appropriate where the information sought from the witness is relevant to the investigation.
The dates on which Jay-Z will appear in court to testify are unknown, as of Thursday afternoon.
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Jay-Z's court appearance could be set aside if he reaches an agreement with the SEC to answer questions.
Jay-Z has been ordered by a federal judge to explain why he shouldn't be ordered to testify in an ongoing investigation by the Securities and Exchange Commission.
Carter will have to appear at a hearing on May 8 to argue why the court should not order his testimony.
Jay-Z has been subpoenaed twice in the case and has ignored both subpoenas.
The 99 Issues rapper continued as chief inventive officer of the Rocawear model after its sale and Iconix entered a separate three way partnership with the star as part of the sale to determine manufacturers to be acquired.
A representative from Iconix did not immediately respond to CNBC's request for comment. It posted a $557 million loss previous year, while annual revenue fell 7 percent to $226 million.