Some 57,000 complaints have been made about the show's coverage of the Oprah Winfrey interview on 8 and 9 March.
On 9 March, Morgan said he "didn't believe" a word Meghan had said. He left the ITV programme later that day.
The total of 57,121 complaints is 12,600 more than those made over a race row on Celebrity Big Brother in 2007.
The duchess herself is among those who have complained to the watchdog.
