"An unauthorised tweet was posted on a government channel this evening. The post has been removed and we are investigating the matter," the UK Cabinet Office posted.
Rowling responded on her Twitter account: "When you find out who it was, let us know. I want to give them a year's salary."
She screenshot the since-deleted tweet and shared it, adding clapping emojis.
The Harry Potter author called Johnson "despicable" for not holding his advisor to account in several fiery posts.
"Watching Johnson. This is despicable. Parents all over this country have abided by the lockdown rules, even while ill themselves.
"Hundreds of thousands managed toddlers while shut up inside cramped accommodation, purely for the common good AS THE GOVERNMENT TOLD THEM TO DO."
"Grieving families have been split, funerals have been unattended, the dying have been forced to say their farewells via iPads, because people obeyed the rules to protect the NHS and save lives, and Johnson stands there defending that utter f***weasel Cummings."
In April, Rowling shared with her social media followers that she had symptoms of Covid-19. She shared breathing tips from a doctor which she says helped her.
She posted: "Please watch this doc from Queens Hospital explain how to relieve respiratory symptoms. For last 2 weeks I've had all symptoms of C19 (tho haven't been tested) & did this on doc husband's advice. I'm fully recovered & technique helped a lot. [sic]"