The chief executive of

Tesla Inc.

and Space Exploration Technologies Corp., or SpaceX—and who is known for sometimes taking swipes at rivals on Twitter—issued a faux apology as part of the host’s customary opening monologue. “To anyone I’ve offended, I just want to say, I reinvented electric cars, and I’m sending people to Mars in a rocket ship,” Mr. Musk said. “Did you think I was also going to be a chill, normal dude?”

The early cracks stopped short of some of Mr. Musk’s edgier comments. In the past, he has taken swipes at the Securities and Exchange Commission and billionaire

Jeff Bezos.

Mr. Musk, who has a history of comments that move markets, had a similar effect on “SNL,” when he appeared in its satirical news segment, Weekend Update, as “Lloyd Ostertag, financial expert,” who called himself “The Dogefather.”

After he expounded on the merits of the cryptocurrency using jargon, cast members

Michael Che

and

Colin Jost

repeatedly asked him to explain, “What is dogecoin?” Pressed by Mr. Che, Mr. Musk eventually said, “Yeah, it’s a hustle.”

The price of dogecoin, created in 2013 as a joke, surged as high as 74 cents early Saturday in advance of Mr. Musk’s “SNL” appearance, spurring hope among investors that it would cross $1 for the first time. The price wobbled between 49 cents and 69 cents for most of the broadcast, according to CoinDesk.

When the show ended, dogecoin was trading around 52 cents, putting its market value at about $72 billion—greater than the valuations of

Kraft Heinz Co.

Meanwhile, Robinhood, the online trading app popular with individual investors, said on Twitter during the program that it was experiencing issues with cryptocurrency trading. Robinhood later tweeted that the issues were resolved.

The stir created around the show since Mr. Musk was named as host last month suggests that “SNL” may see a surge in TV ratings. The show has drawn an average 9.2 million total viewers in its 46th season, according to Nielsen data. NBC said Sunday that Mr. Musk’s episode tied for its third-highest rated telecast of the season, behind Dave Chappelle in November and the season premiere hosted by Chris Rock in October.

NBC sought to capitalize on Mr. Musk’s global notoriety, live-streaming the show for the first time internationally in more than 100 countries.

In the run up to the show, which comes with a battery of sketch writers, Mr. Musk turned to Twitter to crowdsource ideas for his appearance from among his roughly 53 million followers. There the live-comedy novice took some online ribbing from “SNL” cast member

Chris Redd

for referring to a sketch as a “skit.”

Maye Musk made an appearance in keeping with a show tradition of bringing on cast members’ mothers on the eve of Mother’s Day. She said that she hoped her gift wouldn’t be the dogecoin her son has often tweeted about. Mr. Musk said it was.

His appearance on “SNL” is Mr. Musk’s latest excursion into pop culture. His casting credits include a number of film and TV cameos, such as “Iron Man 2” and episodes of “The Big Bang Theory,” “South Park” and “The Simpsons.”

Mr. Musk is one of a small cadre of business people to host “SNL,” which typically taps people from the entertainment world for the coveted role. The late George Steinbrenner, owner of the New York Yankees, hosted in 1990, and

Ralph Nader,

the high-profile consumer crusader, hosted in 1977. Publishing magnate

Steve Forbes

did the honors in 1996, shortly after giving up his pursuit of the Republican presidential nomination.

Donald Trump

hosted in 2004, when he was early in his tenure on the NBC reality series “The Apprentice,” and again in 2015, when he was vying to be the Republican candidate for the White House.

Unlike some hosts who play a more passive role in the comedy, Mr. Musk appeared in the majority of live sketches and prerecorded bits. In one segment, Mr. Musk, who longs to colonize Mars, issued commands to a Mars mission that relied on a slacker character played by

Pete Davidson.

Mr. Musk also showed up in the sketch, “Gen Z Hospital,” playing a bearded doctor and managing to deliver youth slang with a straight face. He also dressed up as the

Nintendo

character Wario for a parody of anti-Italian bias in the Super Mario videogames. In another segment, set in the Old West, his character talked about electric and self-driving horses and attacking the enemy through an underground tunnel, a reference to Tesla cars and his tunnel-digging venture, the Boring Co.

In his opening monologue, Mr. Musk made light of the name of his youngest child, X Æ A-Xii. “It’s pronounced cat running across the keyboard,” he said.

He also joked about a now-infamous incident from a few years ago. “A lot of times people are reduced to the dumbest thing they ever did, like one time I smoked weed on Joe Rogan’s podcast,” Mr. Musk said. “And now all the time I hear, ‘Elon Musk, all he ever does is smoke weed on podcasts,’ like I go from podcast to podcast, lighting up joints.”

In several segments, Mr. Musk played off his socially awkward side, in keeping with his statement that he has Asperger’s. The condition is a form of autism that affects how a person makes sense of the world, processes information and relates to others.

Mr. Musk often has used his large public persona to serve as a way to promote his company’s products, with Tesla forgoing the cost of TV commercials used heavily by many rival car makers. In parallel with the “SNL” appearance, Tesla showed off in New York its coming pickup truck, unveiled more than a year ago with somewhat botched showmanship. Some rival electric-vehicle makers ran ads during the show.

—Paul Vigna contributed to this article.

Write to Rebecca Elliott at rebecca.elliott@wsj.com and John Jurgensen at john.jurgensen@wsj.com

Corrections & Amplifications
The formal name of SpaceX is Space Exploration Technologies Corp. An earlier version of this article incorrectly said Space Exploration Technology Corp. Also, Chris Redd is currently in the cast of “Saturday Night Live.” An earlier version of the article said he was a former cast member. (Corrected on May 9.)