In a California court, Musk had accused the AI firm he helped set up in 2015 of breaching a commitment to creating artificial intelligence that benefits society when it became a for-profit enterprise backed by Microsoft.
A filing by an attorney representing Musk asked the court to dismiss the entire case, without offering a reason.
Neither Musk nor OpenAI had responded to requests for comment at time of publication.
The tycoon, who left OpenAI in 2018, argued in his original complaint that the ChatGPT maker was always intended as a non-profit entity.
But he said recent boardroom changes meant OpenAI was now effectively a subsidiary of software giant Microsoft.
Musk has made similar accusations in the past and both OpenAI and Microsoft have denied them.
OpenAI captured the public's imagination in late 2022 with the release of its chatbot ChatGPT, which can generate poems and essays and even succeed in exams.
The firm has also developed image and video generating tools that are seen as the leaders in their field.
Microsoft, a major investor in OpenAI since 2019, poured billions more into the firm last year.
And the giant firm stepped in when OpenAI's board fired CEO Altman in November last year, hiring him and offering to house any staff members who were unhappy with his ousting.
The OpenAI board reversed course as dissent soared in the company, reinstating Altman and replacing several board members.
OpenAI started life as a non-profit dedicated to developing "artificial general intelligence" (AGI), a vague term loosely defined as a kind of AI that would far outstrip human capabilities on all measures of intelligence.
The idea was for OpenAI to guarantee that such technology would be safe for humanity.
But Musk's legal case said this founding principle had been "turned on its head".
"To this day, OpenAI Inc's website continues to profess that its charter is to ensure that AGI 'benefits all of humanity'," the filing stated.
"In reality, however, OpenAI Inc has been transformed into a closed-source de facto subsidiary of the largest technology company in the world: Microsoft."
Since leaving OpenAI, Musk has joined the chorus of critics warning that superintelligence could spell the end for humanity.
He also launched his own AI firm, xAI, last year and said he wanted to raise $1 billion from investors.
Musk expressed anger with OpenAI on Monday, lashing out at its partnership with Apple.
"Apple has no clue what's actually going on once they hand your data over to OpenAI. They're selling you down the river," Musk said in a post on X, which he also owns.
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