The 26-year old, who made 17 Premier League appearances last season, moved to St. Mary's two years ago from Feyenoord.
Southampton's vice chairman (Football) Les Reed said: "We have an extremely strong and deep group of midfielders, meaning there is significant competition for places in the team.
"We feel it is beneficial to give Jordy the chance to play regular first-team football over the coming months. This move to a strong Club Brugge side will allow him to do that at a high level."
— Club Brugge KV (@ClubBrugge) August 30, 2017