A spokesman said the woman's attacker covered her mouth and dragged her backwards in Spotland Road, Rochdale at about 06:45 BST on Tuesday.
He said she lost consciousness and woke up on the floor having been raped. She then walked to a nearby butchers' shop and told staff she had been assaulted.
Supt Alistair Mallen said it was "vile, wicked and despicable crime".
The woman's attacker was described as white.
Officers are reviewing CCTV footage, speaking to people in the area and carrying out forensic tests.
"I am sure the entire community will share our revulsion at this," Supt Mallen said.
"I now want people... to imagine if that had been your mum or grandma.
"I want to harness these feelings and use them to help the police do their job - catch this man and put him before the courts."

Tom Alexander, who will leave the chief executive role on 31 August, said he wished "to pursue other interests".
He will be replaced by Olaf Swantee, who is currently executive vice president at France Telecom.
Everything Everywhere is a joint venture between Deutsche Telekom and France Telecom.
It started operations in May 2010 when the two companies merged their UK operations.
Telecoms analysts have questioned whether the merger has been carried out as smoothly as had been intended.
Mr Alexander was Everything Everywhere's first chief executive. He had previously held the same position at Orange UK from 2008.
"It's been my privilege to serve Everything Everywhere these past twelve months, and Orange before that," he said.
"Olaf will be an excellent chief executive and leader for Everything Everywhere moving forward."
Mr Alexander will continue in an advisory role at the company until the end of the year.
Mr Swantee is already on the board of Everything Everywhere. Prior to joining France Telecom, he worked for computer maker HP.
Everything Everywhere is the UK's largest mobile phone network operator, with about 28 million customers across the Orange and T-Mobile brands. It has 16,000 employees and 700 stores.
Its number of new contract customers slowed in the first quarter of 2011.
A 90-year-old woman was dragged off a street and raped in Greater Manchester, police have said.
[NEXT_CONCEPT]
The boss of Everything Everywhere, the parent group of UK mobile phone networks Orange and T-Mobile, is standing down for "personal reasons".