The woman had her arms and upper body painted yellow and was wearing a matching headband, apparently imitating the tennis player's outfit for the tournament, and had her face completely painted black.
She and her friend, who was wearing a similar outfit but only had splodges of black on her cheeks, were waving a sign saying “keep calm and be Serena”.
Russell Brown, a journalist from New Zealand, caught the moment they appeared in television coverage and posted it on Twitter.
It has since been shared hundreds of times, sparking a debate about racism and dress code regulations at the Grand Slam.
“It's straight bonkers they let her in,” one person wrote. “They better have kicked her out.”
Another added: “I see no fan. I see an ignorant, disrespectful, fool. Seriously? Is this not 2016?”
Others called the outfit “unbelievable”, “racist” and “terribly insensitive”.
The woman was watching Williams’ match on Wednesday, when the women’s world number one was playing Agnieszka Radwańska in the semi-final.
She eventually beat her fourth-seeded opponent 6-0 6-4.
But Williams went on to be upset in the Australian Open final by Germany’s Angelique Kerber in a three-set contest.
With six Australian Opens among her 69 career titles, Williams had been the overwhelming favourite but was gracious in defeat in Melbourne.
“Let me be the first to congratulate you,” she told Kerber in an on-court speech. ”Enjoy the moment. I'm so happy for you.“
Brushing off criticism in a press conference later in the evening, Williams added: “Every time I walk in this room, everyone expects me to win every single match, every single day of my life.
“As much as I would like to be a robot, I'm not.”
Additional reportin by AP
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