Police said a woman had been arrested at Wyong station on the Central Coast, and issued with a summons for offensive language.
Video posted to YouTube showed the woman mocking the language and facial features of the other passenger on a Sydney to Newcastle train on Wednesday.
The woman has since apologised for the tirade. If found guilty of offensive behaviour, she faces a $500 fine.
Police first spoke to Ms Wilkins on Wednesday when she alighted at Strathfield in Sydney's west but she wasn't arrested until later in the evening.
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Dr Tim Soutphommasane, the Race Discrimination Commissioner with the Australian Human Rights Commission, condemned the attack.
In a statement on Twitter, Dr Soutphommasane praised the passengers who uploaded the video and implored the public to "hold people accountable for racist abuse."
"It is important that we hold people accountable for racist abuse and vilification. When confronted with such conduct, everyone should consider a response, including reporting it to a relevant authority."
Sydney Trains chief Howard Collins said he was "shocked" by the rant and the company would be working with police to investigate.
"I'm just amazed - we've got to stamp this out," he said.