With little to play for other than World Test Championship points, Pakistan made the call to leave out their inspirational leader of the attack in Afridi.
That will allow Pakistan to bring in spinner Sajid Khan, with first-choice off-breaker Abrar Ahmed still nursing a leg injury.
Captain Shan Masood had earlier said the tourists were keen to play two spinners in Sydney.
"We think that it might turn in Sydney. So we want to give ourselves the best possible opportunity to have the best players on the field," Masood said.
"We've kept Abrar on the Australian tour. They have looked after him very well. His rehab process has been going very well.
"We always had Sydney in mind (for him).
"But we have to be absolutely sure he is close to 100 per cent fit ... If not we're taking a risk he doesn't break down over there."
Pakistan had been forced to rely on spinning allrounder Agha Salman, who has taken only one wicket from 51 overs and gone for 160 runs in the two Tests to date.
The call to axe Imam comes after the opener made scores of 62, 10, 10 and 12 on the tour so far.
In his place 21-year-old Saim Ayub will debut.
One other change is guaranteed after Pakistan warmed up without Abdullah Shafique in the slips on Tuesday and with Babar Azam introduced at first slip.
Shafique will play but has been banished from the cordon after his three drops in the opening two Tests.
Masood defended the delay in changing the cordon, with Shafique not ousted until the morning of day four in Melbourne.
"In a game your hands are tied because slips are very specialised," Masood said.
"A lot of fielding places in Test cricket are very specialised. We had four genuine quick bowlers, so it was hard to get them into the slips.
"And then Abdullah Shafique has been a good slipsman for us and those are the guys that practise for hours every day."
"He's a brilliant slips fielder. He's got age on his side. You'll see him standing in the slips more often.
"But I think if he doesn't feel comfortable, Babar is a decent first slipper."
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