The woman, currently a resident of the YWCA in Calgary, asked police not to release her name, the Calgary Sun reported.
"It never crossed my mind to keep the money," she said. "It's not mine to keep. I didn't think keeping it at all."
The woman said she spotted the purse leaning against the door of a car Thursday morning. When the car drove off without it, she first tried to catch the driver's attention and then took it back to the Y.
She said she found the money, $10,400 Canadian or $10,600 U.S., while she was looking for some way to get in touch with the purse's owner. She then consulted her case manager, and they called police.
The money was quickly claimed by an Edmonton woman.
Police Constable Eddie Chesal said there is no reason to believe the owner was involved in anything illegal.
Chesal said the homeless woman acted with unusual honesty: "It definitely could have ended differently had somebody else found it. I spoke with her and she's very humble about it."