On Friday, Rowling expressed condolences to Rushdie by writing "let him be ok" on the social network. Pakistani student and social activist Meer Asif Aziz commented on the post with words "don't worry you are next."
"Police are involved (were already involved on other threats)," Rowling tweeted on Saturday.
After receiving the threat, the UK writer has also contacted Twitter support team, but it has seen no violations of Twitter rules in Aziz's comment.
This is not the first threat against Rowling. Last November, the Scottish police were investigating threatening letters the writer received after three activists posted pictures made in front of her house in such a way that the address was visible. Nevertheless, law enforcement ultimately did not consider the publication of Rowling's address a criminal offense.
On Friday, Rushdie was about to deliver a lecture at the Chautauqua Institution in western New York, when he was suddenly stabbed twice by 24-year-old man Hadi Matar. Rushdie's literary agent Andrew Wylie told media that the author was hospitalized and on a ventilator. On Sunday, Rushdie, was disconnected from the ventilator and is now able to talk, according to fellow author Aatish Ali Taseer.
NBC News reported, citing a law enforcement official, that the preliminary review of Matar's social media showed that he had sympathies for Shia extremism and the Islamic Revolutionary Guard Corps (IRGC). At the same time, the source said there were no "definitive links" to the IRGC.
Rushdie is a celebrated India-born British-American author and winner of numerous literary prizes. In 1989, Ruhollah Khomeini, the supreme leader of Iran at that time, issued an edict calling for the killing of Rushdie, whose book "The Satanic Verses" is considered by many Muslims to be blasphemous.