Dyke, who took up his FA role last month, thinks the tournament is likely to move to winter because of the heat.
The Premier League opposes a change of dates, while Dyke's predecessor David Bernstein said in June that any switch would be "fundamentally flawed".
But Qatar's World Cup organising committee says it is ready to host the tournament in summer.
"Even if all the stadia are air-conditioned, I think it will be impossible for the fans," Dyke said.
"Just go out there and wander around in that sort of heat. I just don't think it's possible.
The Premier League is understood to be surprised and disappointed by Dyke's comments, as it wishes to join forces with the FA in opposing a change of date.
Richard Scudamore, the Premier League chief executive, said in July that switching the Qatar World Cup to winter would cause chaos for football leagues around the world.
His organisation believes such a change would have an impact on the three domestic seasons around the tournament - most notably 2021-22 - affecting broadcast deals and requiring every player's contract to be rewritten.
In 2010 Qatar defeated bids from South Korea, Japan, Australia and the United States to be awarded the 2022 World Cup.
The bid has been plagued by allegations of corruption, although organisers have always insisted they did nothing wrong.