The Harry Potter author described several transgender women as men, including convicted prisoners, trans activists and other public figures.
The new law creates a new crime of “stirring up hatred” relating to protected characteristics.
The force said complaints had been received but no action would be taken.
Reacting to the news, Ms Rowling posted on X: “I hope every woman in Scotland who wishes to speak up for the reality and importance of biological sex will be reassured by this announcement, and I trust that all women – irrespective of profile or financial means – will be treated equally under the law.
“If they go after any woman for simply calling a man a man, I’ll repeat that woman’s words and they can charge us both at once.”
The Hate Crime and Public Order (Scotland) Act 2021 makes it a criminal offence to make derogatory comments based on disability, religion, sexual orientation, transgender identity or being intersex.
Stirring up hatred based on race, colour, nationality or ethnicity was already illegal in Great Britain under the Public Order Act 1986 but is now included in the new law.
Since the law came into effect on Monday Police Scotland has received more than 3,000 complaints.
Prime Minister Rishi Sunak earlier backed Ms Rowling’s stance stating the UK had a proud tradition of free speech.
Mr Sunak would not be drawn on whether he supported her approach, saying that it was “not right for me to comment on police matters, individual matters”.
But he added: “We should not be criminalising people saying common sense things about biological sex, clearly that isn’t right.
“We have a proud tradition of free speech.”
