Mr Musk, the world's richest person, proposed UN-supervised elections in four occupied regions that Moscow last week moved to annex after what it called referendums. The votes were denounced by Kyiv and Western governments as illegal and coercive.
"Russia leaves if that is will of the people," Mr Musk wrote.
He earned the wrath of Mr Zelensky, who proposed his own survey on his Twitter account.
"Which @elonmusk do you like more?," the president tweeted, offering two responses: one who supports Ukraine, one who supports Russia.
Mykhailo Podolyak, adviser to Mr Zelensky, asked Mr Musk in a response: “Will hundred thousand dead in Mariupol vote? Or those who went through concentration camps? @elonmusk you create rockets and dream of colonising Mars. Russia creates mobile crematoria and dreams of Ukrainians disappearing as a nation. It is not a "voting" issue.”
The Tesla chief executive suggested that Crimea, which Moscow seized in 2014, be formally recognised as Russia, that water supply to Crimea be assured and that Ukraine remain neutral. He asked Twitter users to vote 'yes' or 'no' on the plan.
Russia continues to hold the Crimean Peninsula, which it annexed from Ukraine in 2014 after an invasion.
"Dear @elonmusk, when someone tries to steal the wheels of your Tesla, it doesn't make them legal owner of the car or of the wheels. Even though they claim both voted in favour of it. Just saying," Lithuania's President Gitanas Nausėda tweeted in response.
The 51-year-old tech entrepreneur, who is also chief executive of SpaceX, followed up his first tweet with another yes-or-no poll: "Let's try this then: the will of the people who live in the Donbas & Crimea should decide whether they're part of Russia or Ukraine."
He said he did not care if his proposal was unpopular, arguing that he did care "that millions of people may die needlessly for an essentially identical outcome."
"Russia has >3 times population of Ukraine, so victory for Ukraine is unlikely in total war. If you care about the people of Ukraine, seek peace," he posted on Twitter.
In February, when Ukraine's internet was disrupted following Russia's invasion, Mr Musk responded to a tweet by a Ukrainian government official seeking help. He said SpaceX's Starlink satellite broadband service was available in Ukraine and that SpaceX was sending more terminals to the country.
Mr Musk has come to court controversy on social media in recent months.
Ukraine's outspoken outgoing ambassador to Germany, Andriy Melnyk, had a rather more blunt reaction to Mr Musk's “peace plan”. Mr Melnyk faced criticism in July for defending World War Two Ukrainian nationalist leader Stepan Bandera.
"F(***) off is my very diplomatic reply to you @elonmusk," tweeted Mr Melnyk.
“The only outcome is that now no Ukrainian will EVER buy your f…ing tesla crap. So good luck to you.”