The Australian will join up with Barry Fry's side tomorrow and could make his debut against Oldham on Saturday. He will also be available for The Posh in their FA Cup fourth round tie at Nottingham Forest later this month.
McMaster can play as a striker or on either side of midfield.
Defender Robert Constable has made the short trip to Conference side York City, with whom he will also spend a month on loan.
He will be included in the Minstermen's squad for the weekend visit of Morecambe. Constable, 18, is a central midfield player who is equally comfortable in defence.