The multiple Group 1 winner was due to kick off his autumn in the Canterbury Stakes (1300m) at Randwick on Saturday week, but Neasham issued a statement on Thursday confirming that is off the table.
"We would like to advise that Zaaki will not be running in the Canterbury Stakes as planned next weekend," Neasham said.
"While physically he is very sound and healthy, we feel his recent trial and gallops at home have not been satisfactory.
"He will head to the paddock for a short freshen up before we decide what his next options are."
The winner of more than $9.7 million in prizemoney, Zaaki was coming off a fruitful spring carnival which culminated in a Mackinnon Stakes victory.
Neasham had openly stated the gelding performed below expectations when down the track in a Rosehill barrier trial earlier this month and he was again lacklustre in an exhibition gallop between races at Warwick Farm on Wednesday.
While she hopes a stint in the paddock will rejuvenate him, Zaaki is rising nine and any decision on his racing future will be made in the best interests of the horse.
"He has been a star for the stable over the past two seasons and his general wellbeing is our highest priority," Neasham said.
"After trialling very well at the start of this preparation, we hope that a freshen up will see him bounce back to his best."
Zaaki had been prominent in markets to defend his All-Star Mile crown and was an equal favourite for the Doncaster Mile.