The attacker, who missed the second half of last season due to Achilles surgery, had been sidelined recently with a calf problem but was named in the Tigers' starting XI to face Sunderland on Saturday.
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"[It's] put a dampener on everything," the Hull boss told reporters of the "bad news".
"He broke down in the warm-up last week and it's been confirmed there's a tear in his Achilles that will keep him out until at least February.
"There's one or two specialists looking at him and we'll look for the best way forward for him. He's certainly going to be missing for the next eight to 10 weeks, I'd have thought.
"It's tragically hard luck on Sone. He's had a few problems with it before and we thought we were over the situation. It's been an ongoing issue. Whether it's related [to his previous Achilles problems] we're not quite sure."