Dawson limped off with a knee injury during Saturday’s 1-0 win at home to Bolton Wanderers and is awaiting news of a scan taken on Monday.
The defender has only recently returned from a hamstring injury and boss Steve Bruce said: “For him to come off and feel the weight on his knee the way he did, we’re expected at least a month I would think.
“That’s the downside of Saturday, as soon as he came back into the team. He’s a big player for us but we have to be without him.”
With Alex Bruce ruled out for a similar period with a back injury, Harry Maguire and Curtis Davies are Hull’s only fit centre backs.