Chester sustained the problem in the final few minutes of the 3-2 victory over the Magpies at St James' Park on Saturday.
"The injury is what we feared," manager Steve Bruce told Hull's official website.
"We feared it would be six to eight weeks just by looking at him at the time because when you do your hamstring, you can hardly put one foot in front of the other and you feel very, very sore.
"That is how James was in the changing room afterwards. We feared it would be that and the scans have confirmed it.
"I keep talking about needing luck with injuries. We now have (Robert) Koren out for eight weeks and James Chester out for eight weeks - let's hope we can get away with it this week and not pick up any more major ones."
Abdoulaye Faye and Paul McShane are now in line to replace Chester against West Ham on Saturday.
"Tuesday was too early for Paul McShane because he has been out for 10 or 12 days with a hamstring strain," added Bruce.
"We'll see how he is on Thursday but he could possibly be available."