Faye was forced off just before half time in Saturday's game and will be assessed this week.
Boss Steve Bruce said: "Abdoulaye's got a calf problem and we'll see how that is, but it's usually two or three weeks.
"Thankfully, the one area of the pitch where we've been rock solid this season is the three central defenders, whatever combination we've played.
"We've got Jack Hobbs to come in and he did well on Saturday."
Meanwhile, David Meyler has withdrawn from the Republic of Ireland squad for Wednesday's friendly against Poland after picking up a knee injury.
But Bruce is hopeful the 23-year-old will recover in time to help third-placed Hull continue their impressive run of form.
"David got a horrible knock on his knee, although thankfully it looks to be okay," added Bruce.
"When Meyler went down holding his right knee, I feared the worst. He's got stitches, but he looks as though he's going to be okay."