Musk has been a proponent of the cryptocurrency, which was created as a joke in 2013 based on a popular internet meme but has surged to the No. 10 virtual currency in recent days, according to data from CoinMarketCap.com.
"Bought some Dogecoin for lil X, so he can be a toddler hodler," Musk tweeted Wednesday.
Musk tweeted a poll last week that received 2.4 million responses asking users whether the "future currency of Earth" would be Dogecoin or "all other crypto combined." More than 70% of respondents picked Dogecoin.
"The people have spoken," Musk said once the survey ended.
The billionaire has previously tweeted about Dogecoin, including a 2019 tweet in which he referred to it as his "fav cryptocurrency." Musk has expressed interest in other cryptocurrencies, as well, including bitcoin. Tesla said in a Monday SEC filing that the company had invested $1.5 billion in bitcoin and would start accepting it as a form of payment.
After Elon Musk added #bitcoin to his Twitter bio, the price of the cryptocurrency briefly surged around 20% on Feb. 5.
"I do at this point think bitcoin is a good thing, and I am a supporter of bitcoin," Musk said during a live-streamed interview on the popular audio chat app Club House on Sunday. "Many friends of mine have tried to convince me to get involved in bitcoin for a long time."
Musk added: "I think bitcoin is really on the verge of getting broad acceptance by conventional finance people."
The SpaceX founder explained that one friend offered him a slice of "bitcoin cake" in 2013.
Billionaire investor Mark Cuban also shared a Monday statement saying he bought the cryptocurrency for his son, as well.
"Dogecoin is less than a dime. You can buy [$1.00] worth or [$10.00 worth and] have fun watching it all day every day," he said in response to a question about whether investing in Dogecoin is a "bad look." "Literally and I say this with seriousness, it's the best entertainment bang for your buck available."
He continued: "I bought a few dollars for my son and we watch it and discuss all its price movements when they occur. It's fun, it's exciting and educational for him. Some of his friends have gotten into it, as well."
Cuban then clarified that while Dogecoin has no "intrinsic value," it "gives you a better chance of winning than a lottery ticket" all while teaching the economics of supply and demand and introducing people to crypto assets."
The cryptocurrency's market cap has doubled in the last week to more than $9.5 billion, according to CoinMarketCap.
Praise for the cryptocurrency from Musk and other celebrities comes about two weeks after a group of Reddit users banded together and urged people to squeeze short-sellers by investing in shares of falling companies including GameStop; AMC; Bed, Bath & Beyond; and Blackberry, causing their stocks to surge unexpectedly.
The event opened up a discussion about how amateur investors can influence the market and how day trading rules could be reformed.
FOX Business' Lucas Manfredi contributed to this report.