The centre-back suffered a calf injury during last week’s defeat to Swansea, which ruled him out of Saturday’s north London derby draw with Tottenham.
And manager Arsene Wenger has confirmed Tuesday’s clash at the KC Stadium will come too soon for the Frenchman, though he could make a return at the weekend at home to West Brom.
“Laurent will be short for Hull. He has a chance to be available for the weekend, but I think even for then he will be short,” said Wenger.
Goalkeeper Petr Cech will also miss the crucial cup clash.
The Gunners number one recently had positive results from scans on a hamstring problem, but Wenger confirmed he still faces a month on the sidelines.
The boss added: “Petr’s scans were better than expected, but it will still be four weeks for him. So, after the international break.