The incident happened while the woman was walking in Blakenhall and Graiseley when she was approached by a man.
He then attacked her at some point during the night – between 9pm on Saturday, October 12, and 4am on Sunday, October 13.
Detectives are asking anyone who believes they saw the victim or the attacker on the night to contact them.
The man is described as white, around 6ft 2ins tall and at the time was wearing a grey tracksuit top with dark jeans and black shoes. He spoke with an Eastern European accent.
Detective Inspector Gagy Bedi, from West Midlands Police's Public Protection Unit, said: "We are still trying to establish the exact details around what happened and where, so I am asking for anyone who saw a woman walking alone last weekend to speak to us.
“Perhaps you noticed something unusual or saw the woman with a man. She is white, around 5ft 7ins tall, had her dark hair tied up in a ponytail and was wearing a black waist-length coat, dark blue jeans and navy blue trainers with a pink stripe.
“She may have been walking unsteadily on her feet and she hopes that releasing her description will help passers-by remember anything they saw.
"Our specialist officers are continuing to support her."
Police enquiries continue and anyone with information is asked to call West Midlands Police on 101, quoting incident reference number 20WV/242202Q/19.
Alternatively, contact Crimestoppers anonymously on 0800 555111 or at crimestoppers-uk.org