The Blues right-back had been expected to have recovered by now from the injury he sustained during the 1-1 away draw against Sheffield Wednesday on 31st January.
However, Blues boss Alex McLeish has revealed that Parnaby is still at least two-to-four weeks away from a first team comeback.
McLeish told the Birmingham Mail: "He's a couple of weeks, three or four weeks away.
"During his rehab last week he had another setback so it has delayed his comeback."