The 20-year-old has made two first-team appearances at Old Trafford - both in the Capital One Cup this season - and spent last year at Peterborough, where he made 30 appearances.
Tykes manager David Flitcroft revealed that he has tracked the midfielder for the past three years.
The player tweeted: "Delighted to have joined Barnsley on loan for a month. Can't wait to get playing as the belief amongst the manager/players is unreal."
Tunnicliffe will fill the gap caused by Scott Golbourne's knee injury, that has ruled him out for the rest of the campaign, and is available to make his debut against Bristol City this weekend.
Meanwhile, 19-year-old midfielder Jordan Clark has joined League Two side Chesterfield on an emergency one-month loan deal.