The disc-related injury, which has stopped the 33-year-old Queenslander from running, also forced him out of the third and final Test against South Africa in March.
"It's proving a little bit hard to handle at the moment as far as pain," Kasprowicz told reporters Monday.
"The timing at this stage we don't know, the doctors are still investigating what it is and how to fix it."
Kasprowicz was in the running with Stuart Clark, Jason Gillespie, Shaun Tait and Mitchell Johnson for Australia's third seamer's position behind Glenn McGrath and Brett Lee.
Kasprowicz has backed fellow Queenslander Johnson to take the first-change role.
"Mitchell provides a point of difference to that attack, being left-arm, fast and able to swing it," he said.
"That's something exciting that he brings to the (Australian attack)."