Chelsea Wany, 26, had been charged with using threatening and abusive language to cause harassment and fear.
It followed an incident on June 16 last year when police were called to reports of a woman being verbally abusive to a 21-year-old man in the town centre.
Wany, of Station Lane, Berry Brow, appeared at Kirklees Magistrates' Court on Friday.
She was found guilty of the offence and sentenced to 16 weeks in prison.
PC Steve Nicholls, of Kirklees District Police, today said: “Wany used vile and offensive language towards the victim, who was incredibly upset and distressed by the incident.
“We are pleased today with the sentence handed down to Wany and we hope this sentence will be reassuring to our communities in Kirklees that hate crime of any kind is taken extremely seriously by West Yorkshire Police and perpetrators will be dealt with robustly.”