The 43-year-old blonde-haired woman in a red car was filmed yelling racial abuses at the men.
In a statement, the West Yorkshire police said a group of Asian men were walking near to Dewsbury Cemetery when a vehicle pulled up alongside them and a female passenger shouted racial abuse.
The police, however, did not identify the nationality of the men.
A video of the incident shows the woman who is a passenger in a small red car, aggressively targeting the men, the Huddersfield Examiner reported.
The men - identified by local media as Muslims - had reportedly been paying respects at the cemetery as part of Eid rituals when the incident happened on Friday.
"This was an incredibly distressing experience and our enquiries are very much underway to identify those involved. The victims were understandably left shocked and upset following this incident," said Superintendent Roger Essell, Kirklees District Police.
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