The 90cm-long bunny, called Simon, was found dead in the cargo hold when the flight arrived at Chicago's O'Hare airport from London Heathrow.
The airline has had a torrid few weeks of bad publicity, with a passenger left injured after he was forcibly removed from an overbooked flight in Chicago.
Reports in UK media say the 10 month-old giant rabbit was being delivered to a new "celebrity" owner.
United said it was "saddened" by Simon's death.
Animals dying on planes is rare but not unheard of.
