The owners, Michael Dellegrazie and his girlfriend, moved from Phoenix to New York and decided to get on their 8-year-old Pomeranian, Alejandro, on a plane so they could pick up the dog at the Newark airport.
During the stopover in Detroit, Alejandro was held in a loading facility.
"There was a stop in Detroit at 6 a.m. Alejandro was checked in. He was alive, then between 8 a.m. and 8:30 a.m., he was checked again and he was dead," said Dellegrazie's lawyer, Evan Oshan.
Delta spokeswoman Lisa Hellerstedt said the dog was discovered with vomiting and fluids in the cage.
"The family is very upset," said Oshan. "This is essentially the member of your family who died, saying they are upset is an understatement."
Delta issued a statement saying it is "carrying out a thorough review of the situation" and has been working with Alejandro's owners to support them however possible.
"We know that pets are an important member of the family and we focus on the welfare of all the animals we transport," the statement said. "As part of that review, we want to get more information about why this may have happened to ensure that it does not happen again."
The airline also said it offered a veterinarian to evaluate the dog's body.
Other incidents involving dogs related to airlines
Alejandro's death comes after United Airlines had three animal-related incidents in the space of a week in March.
Kwegyirba Croffie of CNN contributed to this report.