The 19-year-old, who began his career in the Fir Park youth ranks, has made 15 appearances since rejoining the club in the summer and has played at full-back, central defence and midfield.
Motherwell manager Stuart McCall told the club's official website: "I am pleased to get Fraser here for another few months; he will provide good competition for the lads at the back - particularly with Steven Saunders returning to the fold too.
"He's young and still learning the game and we've asked him to fill in all over the place and he has done well for himself.
"He was excellent against Georgios Samaras at Celtic Park during the week; his recovery pace is vital in games like that.
"If we want to finish in the top six and push for European places, then everyone will have a role to play and Fraser will be a big part in that."
Another 19-year-old defender, Nicky Devlin, has extended his loan deal from the club to Dumbarton until the end of January.