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.
Meanwhile, the group aiming to take Motherwell into fan ownership have announced three new appointments to their board.
Derek Watson, Dee Cameron and Colin Macinnes complete the line-up of the board of the Well Society, who have a 15 per cent shareholding in the club and will assume a controlling stake when they raise £1.5million.
The group will now press ahead with the process of electing two representatives on to the club board while continuing to recruit new members and raise more money.