"Elon Musk, a word of advice: Don't measure strength against that of Putin's," he wrote, in an English translation shared by Musk.
"Vladimir Vladimirovich (Putin's middle name) will look unsportsmanlike when he beats the hell out of you, a much weaker opponent."
He also snubbed Musk by calling him "gentle (effeminate) Elona" and offered him training in three Chechen institutes: The Russian Special Forces University, the Akhmat Fight Club and the Grozny Chechen State Television and Radio Broadcasting Company.
In response, Musk retaliated with a snarky tweet himself and changed his Twitter name from Elon Musk to Elona Musk.
"Thank you for the offer, but such excellent training would give me too much of an advantage," he wrote.
"If he is afraid to fight, I will agree to use only my left hand and I am not even left-handed. Elona."
Since Russia invaded Ukraine on February 24, Musk has used Twitter to support Ukraine's efforts and denounce Putin's actions.
However, on Tuesday, the world's richest man put his own skin in the game in which he challenged the Russian President to an one-on-one fight.
"I hereby challenge Vladimir Putin to single combat. Stakes are Ukraine," he said, using Russian and Ukrainian language for effect.
"If Putin could so easily humiliate the west, then he would accept the challenge. But he will not," he added.
While the Kremlin didn't respond to Musk's threat directly, the boss of Russia's space agency Roscosmos did weigh in.
"You, little devil, are still young," director general Dmitry Rogozin said in response to Musk's tweet.
"Compete with me weakling; It would only be a waste of time. Overtake my brother first."
Musk then responded with another gibe aimed at Mr Putin.
"I see you are a tough negotiator! OK, you can have 10 per cent more pay per view money," he wrote in response, alongside a picture of a bare-chested Mr Putin riding a bear through a stream, and a photo of himself wielding a flamethrower.
Currently, the photo continues to be Musks' pinned tweet on his Twitter profile.
Prior to this Twitter stoush, Musk supported Ukraine's fight against Russian forces by bolstering the country's communication abilities.
On Friday, the Tesla and SpaceX CEO sent millions of dollars worth of Starlink Rapid Deployment Kits, as well as power adaptors for car cigarette lighters, solar/battery packs and electricity generators.
Currently, on day 20 of the invasion, British intelligence reports that Russian troops are struggling to bolster and support their forces.
In its daily update on the war, the British Department of Defence revealed Russia was "increasingly seeking to generate additional troops to bolster and replace its personnel losses in Ukraine".
"As a result of these losses, it is likely Russia is struggling to conduct offensive operations in the face of sustained Ukrainian resistance. Continued personnel losses will also make it difficult for Russia to secure occupied territory."
While major cities like Mariupol, Kyiv, Odessa and Kharkiv continue to be under Russian shelling and attacks, Ukrainian President Volodymyr Zelensky told citizens on Sunday that their military had "reached a strategic turning point".
"It is impossible to say how many days we still have (ahead of us) to free Ukrainian land. But we can say we will do it," he said.
"We are already moving towards our goal, our victory."
