BBC: The official accounts of Barack Obama, Joe Biden, and Kanye West also requested donations in the cryptocurrency.
“Everyone is asking me to give back, and now is the time,” a tweet from Mr. Gates’s account said. “You send $1,000, I send you back $2,000.”
The tweets were deleted just minutes after they first were posted.
All verified Twitter accounts marked with a blue tick have now been stopped from posting any tweets, and there are reports that password reset requests are also being denied.
Twitter said it was looking into the incident and would issue a statement soon.
On the official account of Mr. Musk, the Tesla and SpaceX chief appeared to offer to double any Bitcoin payment sent to the address of his digital wallet “for the next hour”.
“I’m feeling generous because of Covid-19,” the tweet added, along with a Bitcoin link address.
As well as rapper Kanye West, former US President Barack Obama and Democratic presidential candidate Joe Biden, major companies Uber and the Apple Corporation were targeted.
The accounts of Mike Bloomberg and Kim Kardashian were also hacked.
An unprecedented ‘smash and grab’ operation
By Joe Tidy, a Cyber-security reporter
These “double your Bitcoin” scams have been a persistent pest on Twitter for years but this is unprecedented with the actual accounts of public figures hijacked and on a large scale.
The fact that so many different users have been compromised at the same time implies that this is a problem with Twitter’s platform itself.
Early suggestions are that someone has managed to get hold of some sort of administrative privileges and bypassed the passwords of pretty much any account they want.
With so much power at their fingertips, the attackers could have done a lot more damage with more sophisticated tweets that could have harmed an individual or organization’s reputation.
But the motive seems to be clear – make as much money as quickly as they can. The hackers would have known that the tweets wouldn’t stay up for long so this was the equivalent of a “smash and grab” operation.
There are conflicting accounts of how much money the hackers have made and even when a figure is settled upon, it’s important to remember that cybercriminals are known to add their own funds into their Bitcoin wallets to make the scam seem more legitimate.
Either way, it’s going to be very hard to catch the criminals by following the money and law enforcement, as well as many angry users, will have some strong questions for Twitter about how this could have happened.
Cameron Winklevoss, who along with his brother Tyler was declared the world’s first Bitcoin billionaires in 2017, tweeted a message on Wednesday warning people not to participate in the “scam”.
In a short time, it was online, the address displayed in the tweets received hundreds of contributions totaling more than $100,000 (£80,000).
The Twitter accounts targeted all have millions of followers.