Officers are appealing for witnesses to the hate crime, which happened outside Lincluden Primary School on Thursday.
A woman was walking her children to school when she had to go onto the road to walk round a car that had parked on the pavement, causing an obstruction.
As she walked past, she looked into the 7 seater black VW vehicle, where she saw a female driver. The female driver shouted and swore towards the woman for staring and told her to go back to her own country.
Police are keen to speak to anyone who may have witnessed the incident via the 101 number and quoting ref 2338 of 6th Feb.