The person who dumped the dog has not been caught, the Detroit Free Press reported.
Kevin Hatman, a spokesman for the Michigan Humane Society, said the 2-year-old beagle rescue workers named Gladys (after singer Gladys Knight) is recuperating at the society's Detroit facility.
Hatman said the society had stopped taking names of people interested in adopting Gladys at about 50 calls and she is expected to head to a new home soon.
Gladys, who was howling in pain when she was found, is expected to recover fully.
The beagle stays with animal cruelty investigators during the day and in a cage at night, Hatman said.
"She's kind of walking around and being spoiled," Hatman said. "She has a bit of a cold, but that's the only negative thing we've seen so far."
Gladys had been dumped May 2 in an industrial area.