With the series lost and little to play for other than World Test Championship points, Pakistan opted to leave out their inspirational leader of the attack in Afridi.
That allows them to bring in spinner Sajid Khan in his place on a wicket they expect to turn.
First-choice off-breaker Abrar Ahmed is still unavailable while nursing a leg injury, prompting Sajid's selection.
Pakistan will otherwise retain pace trio Hasan Ali, Aamir Jamal and Mir Hamza from their loss at the MCG last week.
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.
Pakistan relied on spinning allrounder Agha Salman for the first two Tests, with Abrar out and Sajid not picked.
He took only one wicket from 51 overs and went for 160 runs in the losses in Perth and Melbourne, but will have the assistance of Sajid at the SCG from Wednesday.
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.
A tactical change is also 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."
PAKISTAN TEAM FOR THIRD TEST AT SCG: Abdullah Shafique, Saim Ayub, Shan Masood (capt), Babar Azam, Saud Shakeel, Mohammad Rizwan, Agha Salman, Sajid Khan, Hasan Ali, Aamir Jamal, Mir Hamza.
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