After struggling to dislodge John Arne Riise from the left-back role at Craven Cottage, the 21-year-old has moved to Ashton Gate in search of first-team football
The former England Under-19 defender has only made two starts for the Cottagers this season and is looking for first-team football.
He joins the Robins, who are currently winless in six league games and lie in 21st place in the Championship, and he could make his debut when Hull make the trip to Ashton Gate.
This is not the first time Briggs has left Fulham in search of first-team football. He joined another Championship side Peterborough United last season on another short-term deal, making five appearances towards the end of the season.
Bristol City manager Derek McInnes is delighted to have signed Briggs after Greg Cunningham and Liam Fontaine both picked up long-term injuries.
"It's common knowledge that injuries have left us short in defence over the past few weeks and we're delighted to get Matthew on board," McInnes told the club’s official website.
"He'll certainly offer us cover at left-back while Greg [Cunningham] gets himself back to full fitness. Greg is making good progress, but he's nowhere near yet.
"We know all about Matthew because we came close to signing him last season. He spent one training session with us but was called back to Fulham because of an injury crisis.
"He did spend time in the npower Championship with Peterborough in the end last season, so has experience of the division.
"Matthew is quick, energetic and hungry. He's a very highly-rated defender who can play in a number of positions and this loan move works for all parties concerned."