The two clubs had agreed a loan deal but Wilbraham, 26, rejected the move in favour of staying to fight for his place with the Dons.
The former Stockport and Hull City striker has started just 11 league games, scoring three times, since joining MK Dons last season.
Meanwhile, Posh keeper Mark Tyler is expected to be out for another two weeks with his rib injury.
Tyler had another X-ray on his rib injury which revealed a break.
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