The incident, which occurred at approximately 11pm on Sunday (August 13), took place on Valentine Street.
It is reported a male got out of the front passenger seat of the car and pulled the woman into the car before driving away.
Officers are concerned for the welfare of the woman and want to ensure she is found safe and well.
Detective Inspector Andrew Fink from Greater Manchester Police Oldham CID said: "This is an alarming incident and we are working hard to trace this woman to ensure she is safe.
"I want to stress we are treating this as an isolated incident and will have extra uniformed patrols in the area to assist with enquiries and to provide reassurance.
"We are following up a number of lines of inquiry and are also appealing to anyone who may have knowledge of this incident to come forward to police to enable us to check on her welfare.
"You can call 0161 856 8962 or 0161 856 8999 with information, quoting incident number 3716 of 13/08/2023."
Alternatively, you can call the independent charity Crimestoppers on 0800 555 111.
