The Denmark international will be replaced in the role by England international James Ward-Prowse.
Hojbjerg, who has been linked with a move to Tottenham Hotspur, has just over a year left on his contract at the Saint Mary’s stadium.
The 24-year-old joined the Saints from Bayern Munich in the summer of 2016 but has expressed a desire to move to a bigger club.
He told German media outlet SPORT1 last month: "I know what I want, the club knows it too.
“I want to play at an even higher level than I am currently. The relationship between me and Southampton is fantastic.
“The club gave me the platform to grow. I'm not saying 'Goodbye' and I'm focused on my club, but my goal is very clear: I want to win the Premier League and the Champions League."
Speaking in a virtual news conference ahead of Southampton’s return to Premier League action against Norwich City on Friday, manager Ralph Hasenhuttl revealed that Hojbjerg will no longer be skippering the side.
Hasenhuttl said: "No, he will not be captain. I spoke with him and we had an agreement, and made clear that if you decide not to extend your contract, you will not be captain of this team.
"I've spoken to him in the last few days and he knows that he is an important player for this club. I think we have found a good agreement."
Hojbjerg has missed just one league game for Southampton this season.
