The Steelmen currently sit seventh on the SPL table with six points from the same amount of games.
The 20-year-old midfielder has been with United since he was seven and has risen through the youth ranks with the famous club but is now looking to gain some invaluable experience in Scotland.
Speaking to MFC TV, he said: "It's a new experience for me as I've only ever played at Manchester United.
"First of all I'll be looking to get into the side, then I'll be looking to play as many games as possible and try to improve as a player."
He added: "I've watched a few games in Scotland and know it's a good standard and can't wait to get playing."
Motherwell FC is delighted to confirm the signing of @ManUtd's U21 skipper Liam Grimshaw on loan until January. pic.twitter.com/CDxuDgLWcu
— Motherwell FC (@MotherwellFC) September 1, 2015