Dogecoin surged more than 10% early Friday after Mr. Musk’s tweet, before giving back those gains.

Mr. Musk has a record of commenting on cryptocurrencies. Dogecoin’s value jumped late last year when Mr. Musk indicated Tesla would make some merchandise available for purchase using the payment form.

Tesla last year bought $1.5 billion of bitcoin. Mr. Musk also said at the time that the company would begin accepting payments in the cryptocurrency. It later suspended those purchases after Mr. Musk expressed concerns about high levels of fossil-fuel use for bitcoin mining.

Mr. Musk last year said that he and his rocket company, Space Exploration Technologies Corp., or SpaceX, hold bitcoin. The billionaire chief executive said he also owns ethereum and dogecoin, other cryptocurrencies, though those holdings are worth less than his bitcoin stake.

Dogecoin has been one of the most volatile cryptocurrencies. It was started in 2013 as a joke and is centered around a Shiba Inu internet meme. The value of the cryptocurrency surged last year and remains around 2,000% higher than a year ago.

Mr. Musk—the world’s richest person, according to the Bloomberg Billionaires Index—is closely associated with dogecoin. Almost a year ago, he tweeted a faux “Dogue” magazine cover to his millions of followers. He mentioned the currency again on Twitter a few days later, sending its value up 80% intraday, before paring gains.

Dogecoin made a cameo appearance last year in Mr. Musk’s “Saturday Night Live” hosting debut. In a satirical segment, Mr. Musk appeared as “The Dogefather.” After he expounded on the merits of the cryptocurrency using jargon, other cast members asked him to explain, “What is dogecoin?” Pressed, Mr. Musk eventually said, “Yeah, it’s a hustle.”

Write to Robert Wall at robert.wall@wsj.com