Southampton vice-chairman Les Reed told the club's official 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."
Southampton picked up five points from their opening three Premier League games of the season.