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3 year oldThe 49-year-old told viewers he was "the first person with Asperger's" to host the long-running programme - to loud cheers from the audience.
People with Asperger's interpret the environment around them differently to other people.
It is thought to be the first time Mr Musk has spoken about his condition.
The tech boss was guest hosting the sketch show - a coveted role that has been filled by an array of celebrities since SNL's inception in the 1970s. These include Adele, Chris Rock, Ringo Starr, and Will Ferrell.
"I don't always have a lot of intonation or variation in how I speak... which I'm told makes for great comedy," he joked in his opening monologue. "I'm actually making history tonight as the first person with Asperger's to host SNL."
His comment prompted a round of applause from the studio audience.
Mr Musk, who has more than 53 million followers on Twitter, also joked about his use of social media. He has faced criticism and even legal threats over his tweets in the past.
"Look, I know I sometimes say or post strange things, but that's just how my brain works," he said."To anyone who's been offended, I just want to say I reinvented electric cars, and I'm sending people to Mars in a rocket ship. Did you think I was also going to be a chill, normal dude?"
The billionaire also joked about his son's unusual name - he and the singer Grimes announced the birth of their first child, X Æ A-12 Musk, last year. "It's pronounced cat running across keyboard," Mr Musk said.
Later in the programme, the SpaceX CEO spoke about the cryptocurrency Dogecoin.
The currency was created in 2013 by a pair of software workers, and earlier this year it jumped in value by 50% after Mr Musk dubbed it "the people's crypto".
It uses a Shiba Inu dog as its mascot and is based on a meme featuring the animal.
Guest starring … pic.twitter.com/buM3bTOWbX
— Elon Musk (@elonmusk) May 7, 2021
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