Misbah has been in a prolonged slump with the bat, and scored 15 in the second ODI following a duck in the first.
Pakistan were swept 3-0 in the one-day series.
PCB Chairman Shaharyar Khan said it had been Misbah's decision not to play on Sunday and that he was 'depressed' after a poor run of scores.
"Misbah decided that he needed a break from the rather depressing scores he has had in Sri Lanka as well as here," Khan said in a report posted on the board's website (pcb.com.pk).
"The management also agreed that if you want to sit this out it is your decision.
"No one coerced him into doing this. He himself decided that this is the right time for him to take a break and see if he can recover in the tests.
"He is depressed at the fact that he hasn't been scoring and I found it very, very noble on his part that he said 'if the day I get an idea that the team is suffering because of me, then I will myself say, let me go.'"
Australia play Pakistan in a two-test series, with the first starting in Dubai on Oct. 22.
Khan said he had told Misbah he still had the board's firm backing.
"I told him, we appointed you till the World Cup," he added.
"We were criticised for it and we will be now, even more, as he has not scored runs. But we remain totally firm that we have put our bandwagon behind him and (he) will lead.
"I had a half-hour chat with him.
"(I said) if you yourself think your leadership will not deliver, then it is up to you. We will not push you out. This is the view of all three of us – (coach) Waqar Younis and (manager and chief selector) Moin Khan.
"Misbah is determined to put things right, if he does he is back but (we) considered other names of course as a contingency plan."
(Writing by Ian Ransom; Editing by Peter Rutherford)
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