Police are asking for anyone who has information, CCTV or dashcam footage of the incident on Carlinghow Lane on Tuesday, March 8, to come forward.
Emergency services were called there at 10.20pm last night and have said they are concerned for the welfare of the woman.
It is believed that the car involved was a Volkswagen which was seen driving off in the direction of White Lee Road.
Detective Inspector James Bellhouse of Kirklees CID, said: “We are conducting a number of enquiries into this report to build a better picture of what took place and would like to speak to anyone who can assist us.
“My focus very much is for the welfare of the woman involved and I would ask that she or anyone who can provide more details contact us as a priority.
“Carlinghow Road is a busy area and it is likely drivers would have been going past at the time this incident took place and possibly captured dashcam footage.
“Anyone who has footage or can assist our enquiries is asked to contact Kirklees District CID on 101 referencing police number 13220126798."
People can also report information on West Yorkshire Police's website or by calling the independent charity Crimestoppers on 0800 555 111.