The tweet, sent just before 11am, read: “Breaking News: President Trump is injured in arm by gunfire
The message has since been deleted.
A person who answered the phone at the BBC Northampton newsroom on Saturday confirmed the message was sent from its official account.
They said that the corporation was aware of the problem and that it was being “sorted out”.
“Obviously someone has hold of it [the Twitter account] who shouldn’t have,” the person told The Huffington Post UK.
The tweet remained on Twitter for at least 15 minutes before being deleted.
The account later posted an apology confirming the hack.
A BBC Spokesperson said: “BBC Northampton’s Twitter account was hacked this morning. The tweet was removed quickly, as soon as we realised the situation. We are investigating and taking steps to ensure this does not happen again.”