Spector will have a scan on his thigh after being forced to pull-up sharply on the training field.
In recent games the 27-year-old international has played as part of a back three, but he has also stood in at right-back and in midfield this season.
"He’s been one of our most consistent performers this season and we’re gutted for the lad," said Blues boss Lee Clark.
"Whether it’s a torn thigh muscle or a thigh strain we’re not too sure of the extent at this moment.
"I think he’s having a scan today, but he will certainly be out for a minimum of two months and possibly three. We’ll know the diagnosis in the next 24 to 36 hours.
"It was innocuous (the way it happened). It was on the training pitch and he was sprinting for the ball and he pulled up very quickly with nobody near him.
"It’s a massive blow to me not just because of the way he’s been playing, but also because he’s played well at centre-back, right wing-back and in midfield, so we're basically losing two or three players because he’s so versatile."
Read a match preview ahead of Sunday's Sky Bet Championship game against Leeds United here.