According to the article, Musk's three companies, Tesla, SolarCity and SpaceX, "have benefited" from a total of about $4.9 billion in government subsidies. Musk said that the article was misleading and did not accurately portray the situation.

"The article makes it seem as though my company is getting some huge check, which is fundamentally false," he told CNBC's " Power Lunch ."

Musk said that "none of the incentives are necessary, but they are all helpful," referencing incentive packages some of his companies received to build factories in states like Nevada. He said that the reason these incentives exist is because "voters want a particular thing to happen, and faster than it might otherwise occur."

"That is all that these incentives achieve," he added.

Musk said that the only incentives he bargained for directly were state-level incentives. These include a small launch site in Texas for SpaceX and a Tesla gigafactory in Nevada. He explained that such incentive packages have existed long before his companies received some of them.

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"The incentives that Telsa and SolarCity receive are a tiny, tiny, pittance compared to what the oil and gas industry receives every year," he said.

Brian Thevenot, deputy business editor at the Times, responded to Musk's comments by saying that he doesn't need to defend the story because it speaks for itself.

"I'm actually surprised that he had such a sensitive reaction to this story because, really at its core, it's basically a business strategy story that's merely factual," he said in an interview on CNBC's "Closing Bell."

"It paints a picture that I think Elon Musk would agree with, that his business strategy is to incubate high-risk, high-tech companies that promote green technology with the help of billions of dollars of government money," he said.

Thevenot added that the point of the story was to report on the strategy and "let the public debate whether it is wrong or right."

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Speaking on the affordability of a Tesla vehicle, Musk acknowledged the Model S is a "relatively expensive car," but that a more affordable car is expected to come out in 2017. Customers purchasing Model S and Model X cars this year are directly helping to fund a more affordable electric car in the future, he said.

"I wish we could have gotten there sooner, but we are doing the best we can," Musk said.