The teenager joins Posh team-mate Peter Grant at the Conference North side.
"It is important for the development of the young players that they have opportunities to play first-team football," said manager Darren Ferguson.
However, Peterborough chairman Darragh MacAnthony believes McDonald should be playing at a higher level and took to Twitter to question the scouting networks at clubs in the Conference and League Two.
He said: "I cannot believe there is not a queue of clubs in L2/Conference Premier to sign young Shaq on loan.
"He averages two goals a game nearly. Poor scouting! Look past his age scouts/managers."