Odds were slashed from 5/1 to odds-on on November 23 after the influx of high stakes and the market was later suspended after more money piled on Meghan having two children.
Paddy Power, a betting company, believes someone, possibly a punter, has inside information after the sudden stream of "big money" wagers.
The bookmakers say they have been forced to refuse to take any further bets with the price was as high as 5/1 before the suspension.
A spokesman for the Irish bookmakers said: "We had to suspend betting. We saw an almost identical pattern of betting before the announcements of the couple's engagement and pregnancy.
"An unprecedented amount of bets on Meghan and Harry to have twins has forced us to stop taking bets on the market altogether this morning.
"Since the day began, the stream of bets has led us to believe that perhaps the punters - or an insider source - knows something more than we do."
The Royal Family are yet to comment on the influx of betting.
Watch below, Prince Charles teases Aussie names for Harry and Meghan's Royal Baby: