The 29-year-old Dane picked up the injury during training, with the club's official statement describing the diagnosis as a significant muscle problem in the thigh.
Head coach Daniel Thioune did not hide his disappointment at losing one of his most influential players.
"Jens is an absolute leader for our team, on and off the pitch," Thioune said, according to the club's announcement, adding that Stage is expected to be sidelined for "several months."
The timing carries an ironic edge: Hoffenheim had spent recent weeks pursuing Stage, but ultimately judged a transfer too expensive to complete before the market closed. Werder Bremen had been relieved to keep hold of their midfielder as a result, only for that relief to be tempered almost immediately by news he will now be unavailable for a large chunk of the season regardless.
With the transfer window still open until Tuesday, the club may yet need to consider bringing in cover, even though other areas of the squad had been the priority for any remaining incomings.
Stage has been one of Bremen's most reliable performers over the past two campaigns, and his absence leaves a gap in central midfield that will not be easily replicated given the club's limited remaining transfer budget.
The injury adds to what has already been a difficult period for Werder on the fitness front, with the club managing several other muscular and long-term issues across the squad heading into the new season.
The setback struck at the worst possible moment, coming in the final training session before Sunday's Bundesliga opener at Freiburg, when Stage clutched his thigh during a passing drill and had to be driven from the pitch.
Having top-scored for Bremen in each of the past two seasons and been named the club's Player of the Year, he had entered the campaign as arguably the squad's most important attacking outlet, making the timing of the injury - just as talk of his own departure to Hoffenheim had finally died down - all the more painful for Thioune's side.