Alejandro was found dead in his crate in the cargo facility at Detroit Metropolitan Airport, southwest of Detroit in Romulus.
Alejandro is the latest dog to be lost or killed on a cross-country flight.
It's still unclear what caused the dog's death.
Delta released a statement saying they are conducting a thorough review of the incident. "The family now has Alejandro and we continue to offer our support", it added.
The flight was scheduled to travel from Phoenix to Detroit and then to Newark, the spokesperson said.
Delta told WXYZ-TV that Alejandro was checked on by flight staff at 6 a.m. on Wednesday, but when the flight attendant returned to check on the dog two hours later, he was dead. Delta disputes this, noting it was Alejandro's owners who chose to put the dog in a kennel.
The airline said that it was investigating the events leading up to the dog's death.
"We know pets are an important member of the family and we are focused on the well-being of all animals we transport", Delta said in a statement.
Evan Oshan, the attorney for Alejandro's family, told TMZ Delta has been telling people to check their dogs in the cargo hold to avoid confusion with service dogs at the gate.
In March, a French bulldog called Kokito died on a United Airlines flight from Houston to NY after a flight attendant told the owner to put the dog, which was in a carrier, in the overhead locker. A flight attendant told the owner to put him in the overhead bin rather than under the seat. "That's all I can think of", Dellegrazie told CNN. The changes don't affect pets in the cabin. "United Airlines does not care about the safety of their furry travelers".
A day after that incident, a 10-year-old German shepherd named Irgo was flown to Japan when he was supposed to end up in Kansas. In 2017, 506,994 animals were transported on USA airlines, and of those, 24 died, according to Department of Transportation figures.