Australian midfielder Garcia sustained a knee injury during the first half of last week's goalless draw at Crystal Palace and is expected to miss out.
Veteran playmaker Barmby is definitely out due to a leg infection and striker Cullen has been ruled out due to a twisted ankle sustained in training.
Central defender Daniel Ayala is still struggling with a hamstring injury, but another centre-half, on-loan Anthony Gerrard, is expected to prove his fitness after being forced off against Palace with a calf injury.
Tigers manager Nigel Pearson has no other new injury or suspension problems as his side look to stretch their unbeaten league run to six matches.
Source: PA
Source: PA