The 33-year-old Cairns is nursing a hamstring injury he suffered while bowling in the opening game against India last Thursday, which was abandoned due to rain.
Cairns participated in a net session on Tuesday but New Zealand captain Stephen Fleming said he would not be playing.
"He is coming on well, but not well enough for this game," Fleming told reporters.
Cairns bowled three sharp overs in the Madras game, claiming the wicket of opener Virender Sehwag before breaking down.
It was the latest in a series of setbacks for Cairns, who was looking to contribute as a bowler after playing in this year's World Cup mainly as a batsman owing to a long-term knee injury.
Australia captain Ricky Ponting revealed that Kasprowicz has a sprained hip muscle.
"It's unfortunate," he told reporters. "We are keeping a close watch on him."
The injury has further weakened the world champions' pace bowling department after Glenn McGrath, Jason Gillespie and Brett Lee were forced to miss the trip due to injury.
Kasprowicz was called up as a last-minute replacement because of his experience of playing in India.
