A passenger on the Houston-to-New York City flight posted on Facebook that a flight attendant "insisted" the dog be placed in the overhead compartment.
"They assured the safety of the family's pet," June Lara wrote. "So wearily, the mother agreed."
The dog remained in the bin for the three-hour flight and was not given any water, according to Lara. Upon landing at LaGuardia Airport, Lara said the dog was unresponsive.
The airline said in a statement to ABC News it assumes full responsibility for the incident. They could not say if anyone has been disciplined as a result of the incident, as the investigation is ongoing.
"This was a tragic accident that should never have occurred, as pets should never be placed in the overhead bin," United Airlines said in the statement. "We assume full responsibility for this tragedy and express our deepest condolences to the family and are committed to supporting them. We are thoroughly investigating what occurred to prevent this from ever happening again."
United spokesman Charles Hobart said United refunded the tickets purchased for the dog owner and her two children and the fee that they paid to bring a pet on board - typically $200.
The dog was in a small pet carrier designed to fit under an airline seat. It is unclear why the carrier was not placed under a seat, Hobart said. Passengers reported that they heard barking during the flight and didn't know that the dog had died until the plane landed.
According to Department of Transportation statistics on animal incidents on U.S. carriers, United has the highest rate of incidents involving loss, injury or death of animals during air transportation, with 2.24 incidents every 10,000 animals transported.
The Associated Press contributed to this report.