The First Minister, who has 254,000 followers on Twitter, said “people who disagree are not anti-Scottish”.
Ms Sturgeon spoke out after Scotland’s last-minute defeat to Australia in the quarter-final of the Rugby World Cup, when hostile comments were directed at Rowling after she tweeted her support for the national team.
An independence-supporter tweeting as Wings Over Scotland questioned the right of Rowling to support the Scotland team because she helped fund the pro-Union Better Together campaign ahead of least year’s referendum. The political blogger wrote: “You don’t think we’re a nation at all.”
The comment, which was also directed at Scottish writer Muriel Gray, attracted much criticism on Twitter, including from those who backed Yes in the referendum.
Ms Sturgeon, in a tweet, said: “Note to my fellow independence supporters. People who disagree are not anti-Scottish. Does our cause no good to hurl abuse (& it’s wrong).”
Ms Sturgeon warned earlier this year the so-called cybernats who are members of the SNP and who “cross the line” could be disciplined by the party.
Rowling, a Labour supporter, has been branded a “traitor to Scotland” and “Blairite scum”, while fellow celebrity Sir Chris Hoy was called “a traitor” and a “typical Scots Tory naysayer” after he spoke out about the lack of training facilities in Scotland.
Meanwhile, Conservative MSP Alex Johnstone said: “Scotland’s rugby community is not politically divided and the fact that this lunatic fringe is attempting to impose its prejudices on them shows the naivety of those involved.”
Scottish Liberal Democrat leader Willie Rennie said yesterday : “This is not new and not the first time that Nicola Sturgeon has reprimanded her own supporters for their online abuse but it is refreshing nonetheless, as they used to deny that there was ever a problem. This reveals the scale of the problem for the nationalist movement, which has been infected by large numbers of people who believe the way to win an argument is to be offensively aggressive online.
“My message to the nationalist movement is that we will not be browbeaten.”