THE mother who gave her child an inflammatory banner to hold up during the Muslim riot told police she didn't know what "behead" meant.

The Jordanian woman, 28, handed herself in to police on Monday after her photo was splashed across newspapers and TV and she was branded an irresponsible mother.

The woman was photographed encouraging her four-year-old son to hold up a sign which read "Behead all those who insult the prophet".

NSW Police Commissioner Andrew Scipione said the image of the child calling for beheading of another person was "incomprehensible", while Premier Barry O'Farrell called for the woman to be investigated by child protection services.

But the woman, who has only been in Australia for two years, told detectives from strike force McAllister she did not know what the sign meant.

She said she picked up the sign in Hyde Park and, after waving it herself for a short time, gave it to her young child to pose with.

"She said she didn't know what behead meant," a senior police source said.

"She recognised the word 'prophet' and assumed it was something in support of him."

The woman told police she was "embarrassed" by the fuss she had caused.

Originally published as Word 'behead' went over mum's head