Security guards swiftly pounced on the protester, who was wearing a beanie and casual clothes and dragged her away.
“Officers from the Murray River police district placed the woman under arrest after she allegedly threw an egg at the prime minister during a Country Women’s Association event at Albury Entertainment Centre,” the police statement said.
“The egg appears to have struck the prime minister on the head,” police said.
They did not disclose the protester’s name.
Morrison rubbed his head briefly after the egg was tossed and then helped an elderly woman who was pushed to the floor in the scuffle, television images showed.
No injuries were reported, the police said.
“We will stand up to thuggery whether it’s these cowardly activists who have no respect for anyone, or militant unionists standing over small businesses and their employees on work sites,” Morrison said in a message on his Twitter feed.