The 27-year-old, whose last international appearance came against Ireland in June, will undergo surgery later this week and is expected to be sidelined for at least four months.
Newby said: "I'm desperately sad I can't continue with Otago this year, I would love to have played in the Ranfurly Shield challenge against Canterbury but at this level you have to be 100 per cent and I wasn't."
Otago coach Steve Martin added: "He's been troubled by the shoulder for a while now and it was a difficult decision to have the operation, but it was the right thing to do.
"We'll miss him, but it's fortunate that we have two very able vice captains in Josh Blackie and Neil Brew and a core leadership group within the team."
Martin is expected to appoint either flanker Blackie or centre Brew as the team's new captain later this week.