Fleming has been ill since returning home from his team's triumphant tour of Bangladesh and although the ailment has not been diagnosed, he has been ruled out of the four-day match against New South Wales starting in Sydney on Thursday.
The Kiwis have also lost their front-line spinner Daniel Vettori to a shoulder problem but coach John Bracewell said he would still play in the first Test with Australia starting in Brisbane on November 18.
"There is no doubt that Daniel Vettori will be available for the first Test match and this short break is actually a good chance for Daniel to rest after a heavy work load in Bangladesh," he said.
Bracewell also said Fleming was expected to make a full recovery in time for Brisbane but Craig McMillan had joined the squad as cover just in case.
"While we believe that Stephen will be right for the Test match it is important that, with it being such a short flight, we have someone like Craig to come and join the team," Bracewell said.
"He has battled hard in Bangladesh and his arrival gives us cover in the middle order should we need it."
With Fleming and Vettori unavailable for the match against NSW, Scott Styris was promoted to captain the side.
Team: Scott Styris (captain), Mark Richardson, Mathew Sinclair, Hamish Marshall, Nathan Astle, Jacob Oram, James Franklin, Gareth Hopkins, Paul Wiseman, Ian Butler, Chris Martin.
