He made only 16 Premier League appearances last term and has yet to feature under Mauricio Pellegrino, prompting links with a possible move to Crystal Palace.
Saints have allowed the 26-year-old to join the Belgian Pro-League leaders, which they say will help to foster a stronger relationship between the clubs.
Vice-chairman Les Reed told the club's website: "We have an extremely strong and deep group of midfielders here at Southampton, 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.
"This is also an opportunity to develop a relationship for the longer term with Club Brugge, one of Europe's top football clubs, who regularly qualify for European competition.
"We will remain in regular contact with Jordy throughout the loan spell and will be closely monitoring his progress and performances during his time in Belgium, as we do with all our loanees.
"We wish Jordy and Club Brugge the very best for the rest of the season and hope to see him help them to another Jupiler Pro League title."