The cryptocurrency climbed as high at $0.40 (£0.28) from lows of $0.29 earlier in the day after a brutal sell-off on Wednesday.
Musk tweeted: “How much is that Doge in the window?”, with a picture of the Shiba Inu dog from the “doge” meme, from which the coin takes its name and logo, on a dollar bill.
It comes just hours after the cryptocurrency market plummeted into the red, shaking investor confidence.
News of a renewed crackdown in China was blamed for the fall in prices, as the country's central bank issued a statement on its WeChat account reiterating that financial institutions should not accept or deal with cryptocurrencies.
However, prices had been under pressure since Musk said Tesla was abandoning plans to accept bitcoin (BTC-USD) as payment last week.
He cited the environmental impact of bitcoin mining as the reason behind the unexpected U-turn.
The billionaire said he still believed in crypto but remained concerned about bitcoin's energy usage. According to Cambridge University, bitcoin mining accounts for 0.7% of the world's electricity consumption.
Watch: Bitcoin falls below $37,000, dogecoin drops over 40% in crypto bloodbath
Read more: How bad is bitcoin for the environment?
"To be clear, I strongly believe in crypto, but it can’t drive a massive increase in fossil fuel use, especially coal," Musk wrote on Twitter.
"We are concerned about rapidly increasing use of fossil fuels for bitcoin mining and transactions, especially after coal, which has the worst emissions of any fuel."
Bitcoin dropped as low as $32,000 on Wednesday, while ethereum (ETH-USD), the world's second biggest cryptocurrency, also fell as much as 30% during the session.
Data provider CoinMarketCap.com revealed that the value of the entire cryptocurrency market had fallen by 20% over 24 hours, wiping approximately $350bn off the market's value.
Wednesday's sell-off once again highlighted the extreme volatility that characterises the cryptocurrency markets. Unlike with past corrections, analysts said this week's slump had more consequences for the mainstream financial system and traditional companies.
Several institutions have invested billions of dollars into cryptocurrencies, including MicroStrategy (MSTR). Traditional financial firms like PayPal (PYPL) and Goldman Sachs (GS) have also begun handling the asset on behalf of clients, leaving them with potential exposure.
Watch: What are the risks of investing in cryptocurrency?