Musk sent a message about his political affiliations and then added a second message saying he was buying Manchester United.
The club's fans have been critical of the team's performance in recent years.
When asked by a follower if he was serious, Musk replied: "No, this is a long-running joke on the social networking site." I don't want to buy any sports teams.
Musk ran afoul of the US Securities and Exchange Commission when he claimed that he had the funds to take the company private.
That led to a securities fraud settlement that required him to get approval from aTesla attorney before he wrote anything.
He is facing more legal troubles over the deal to buy the social networking site.
Musk lined up a diverse group of other investors to back him after selling a large amount of his shares in the company.
Last month, the deal fell apart after Musk said that he wasn't given enough information about the number of fake accounts on the platform.
He agreed to pay a $1 billion break up fee, but instead of trying to force him to complete the purchase, he's sued. The case is going to be tried in Delaware.
Under Sir Alex Ferguson, United won 13 titles and two trophies, making them the biggest team in the world.
The team hasn't won a trophy since Ferguson retired.
Fans staged protests against the Glazer family after United finished behind Manchester City.
Many supporters in the club's huge international fan base have opposed the Glazers since they took control in 2005, in part because they financed the takeover by putting the club in debt.
Saturday was the latest low in United's history. It was United's second loss to start the season and they are bottom of the league.
The owners of Manchester United were condemned by a fan group.
The fan club said that what they had seen tonight was an embarrassment for the fans.
It was not a surprise. It feels like it's the end of a long journey.
The owners of the Club are mostly to blame for the new low in our decade of decline.