Kostecki had been battling a virus in the days leading up to the event and was absent from the pre-event parade.
Following Race 2 on Saturday, he was taken to the on-site medical centre where he received medical treatment.
Kostecki was trackside on Sunday morning at Hidden Valley Raceway but has elected not to race on medical grounds.
His Enduro Cup co-driver Todd Hazelwood will take the reins of the #17 Shell V-Power Racing Team Ford Mustang.
“Brodie Kostecki will not participate in any Supercars sessions on Sunday at the Darwin Triple Crown,” Dick Johnson Racing said in a statement.
“Brodie was assessed by Supercars Medical Delegate Dr Carl Le this morning following the virus and dehydration that caused him to be taken to the medical centre after finishing in third place in Saturday’s Race 18.
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“Although he received clearance to drive from that issue, lingering after effects have rendered him unable to participate in the rest of the weekend.
“Shell V-Power Racing Team endurance co-driver Todd Hazelwood will drive Car 17 in Kostecki’s place in qualifying and Race 19.”
Dick Johnson Racing team manager Tom Moore said Kostecki made the call not to race after waking up on Sunday morning unwell.
“He went to bed fine last night, had the fluids in him. We thought he was definitely on the mend, and then this morning he unexpectedly woke up unfit to compete safely,” Moore explained.
“He made the decision himself to withdraw from today’s racing.
“You can imagine how hard a decision that would have been to make being the competitor that he is. It’s unfortunate for the team, but we’ve got more things to think about.
“Townsville is only in two weeks time so there’s a long season to come and we’re not going to put anyone in danger out there.
“Todd will get in the car later. He’s getting all sorted out now. Driver ballast, suit, all that sort of stuff and those forms we’ve got to fill out with Supercars.
“He’ll be qualifying the car this morning and racing later this afternoon.”
Qualifying for Race 3 of the Darwin Triple Crown gets underway at 11:15am AEST.
That will be followed by the Top 10 Shootout at 12:00pm AEST.
Race 3 of the weekend at Hidden Valley Raceway is scheduled for 3:10pm AEST.
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