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."
A 90-year-old woman was dragged off a street and raped in Greater Manchester, police have said.