The victim, in her 50s, was approached by a woman while she walked along King Cliffe Road, Birkby, at about 3.20pm on Wednesday.
The suspect grabbed the victim's bag and pulled it away, causing her to fall to the floor.
She then threatened the woman and a struggle ensued.
The suspect fled from the scene after the victim shouted for help.
Detective Constable Rav Rai, of Kirklees District CID said: “Thankfully the victim was not injured during the incident and property was not stolen, however it has clearly been very distressing for her.
"I would appeal to anyone who may have any information or who may have been in or around the area on Wednesday afternoon and may know, or have seen anyone matching the suspect’s description or acting suspiciously to come forward. Our enquiries in to this incident are very much ongoing.”
The suspect is described as a white woman, in her late 20s or early 30s, of skinny build, with a pale face.
She had light brown/mousy-coloured long hair, tied in a ponytail and was wearing a long, knee-length black coat.
Anyone with any information is asked to contact police on 101, quoting reference 13180039206.
Information can also be passed anonymously to the independent crime fighting charity Crime Stoppers on 0800 555 111.