As of Tuesday afternoon more than 50,000 people had retweeted the post and it had received more than 60,000 likes.
The fake account also asked Twitter users to share their Venmo and Paypal account emails as a public response to another tweet and encouraged one user asking for money to send a private message.
Missler sent a tweet from his actual Twitter account "@TheShaneMissler" shortly after he won the lottery prize, warning of fake accounts using his name.
"Unfortunately many fake accounts have already circulated. My only active and real accounts are Instagram and Twitter both @TheShaneMissler," he wrote.
The Florida Lottery announced Missler had claimed the $451 million Mega Millions jackpot prize on Friday, marking the fourth-largest jackpot in the game's 15-year history.
He elected to receive roughly $282 million in a one-time payment to collect his winnings.
While the fake Twitter account offered to pay out a total of $250 million among 50,000 followers, the real Missler will only receive about $211.4 million after federal income taxes.
The account offering money to its followers appears to have been deleted, but other accounts impersonating Missler remain.
