Even before his arrest, Shkreli had quickly become a reviled caricature of Wall Street greed due to actions he took as founder and CEO of Turing Pharmaceuticals. In particular, Shkreli's company purchased the license to Daraprin, a powerful drug that is commonly used to treat HIV, and promptly raised its price by more than 5000 percent, from $13.50 a pill to $750 a pill.

While Shkreli, in the face of stinging criticism from leaders across the political spectrum, announced he would lower the price of the drug and offer steep discounts to providers and insurers, he was also adamant that his role as a pharmaceutical executive was to make money for shareholders, rather than to advance public health.

But Shkreli's arrest complicates the Congressional committee's plans to make the tycoon talk.

Because of the charges against him, Shkreli has argued that requiring him to testify before the committee might violate his fifth amendment right against self-incrimination.

"Counsel informed our Committee that Mr. Shkreli was categorically invoking the 'Act of Production Privilege' under the Fifth Amendment," tweeted Sen. Susan Collins, R-Maine, the chair of the Senate Special Committee on Aging, which is also investigating drug prices.

"Absent a valid justification for the grounds for invoking the Fifth Amendment, Mr. Shkreli's assertion could hinder our investigation," Collins added on Twitter.

Collins and others will likely argue that Shkreli's requested testimony on drug prices has nothing to do with the fraud charges he faces, and therefore is not protected by the fifth amendment.

Other drug executives who are being called to testify include Howard Schiller, the CEO of Valeant Pharmaceuticals, which has bought and dramatically raised the prices of a number of specialty drugs.

"Mr. Schiller looks forward to testifying and sharing with the committee how Valeant works to make its drugs available to the millions of patients who depend on them," said Laurie W. Little, a spokeswoman for Valeant, told the New York Times.