The incident happened on a United Airlines flight between Houston, Texas and New York on Monday.
The airline has said in a statement that they accept full responsibility for the death of the dog.
The French Bulldog was travelling with its owners, a woman and her two children. The dog was being carried in an airline-approved pet carrier case, according to the BBC.
The stewardess claims she was unaware that there was a dog in the carrier bag.
Maggie Gremminger tweeted:
"I want to help this woman and her daughter. They lost their dog because of an @united flight attendant. My heart is broken."
Maggie told the travel website One Mile at a Time that the passenger was repeatedly told to put the dog in the storage compartment. "I witnessed a United flight attendant instruct a woman to put her dog carrier with live dog in an overhead bin. The passenger adamantly pushed back, sharing verbally that her dog was in the bag. "
"By the end of the flight, the dog was dead. The woman was crying in the airplane aisle on the floor."
United Airlines have said they are investigating the dogs death.
United Airlines has a poor record of transporting animals, the Guardian reports.
It had the highest number of animal deaths for any US carrier in 2017 - 18 were killed and 13 injured in while in transit with United last year, according to the US Department of Transport.