Sangha broke his collarbone diving stop a boundary late in Sunday's tight loss to the Melbourne Renegades and appeared in extreme discomfort as he left the pitch with the assistance of a trainer.
The 23-year-old played no further part at Marvel Stadium, replaced in the field by Toby Gray.
An X-Factor player in the most recent BBL team of the tournament, Sangha told AAP he was not holding out hope of playing for the Thunder again this summer, given most collarbone injuries take at least six weeks to heal.
Chris Green has been named acting captain, having filled the role last summer when Usman Khawaja was unavailable.
"Our thoughts are with Jason," Green said in a statement.
"He's a big part of this team as captain, and an even bigger part as a batter - we saw what he did last year in his damaging role in the top order.Â
"The squad is thinking of him at this time because any injury is tough."
While the Thunder prepare to face the Strikers in Adelaide on Tuesday, Sangha was booked to fly back to Sydney on Monday afternoon to begin his recovery and consult with a specialist, who will help determine his return-to-play timeline.
The match will be the Thunder's chance to avenge Friday's heavy loss to the Strikers, when they were bowled out for the lowest total in professional men's T20 history - 15 runs.
The Thunder have not yet confirmed whether they will go to market to replace Sangha.
Burns will miss the remainder of the BBL with the hamstring tear he suffered in the tournament opener against the Thunder last Tuesday.
After testing positive for COVID-19 that day - and being allowed to play under the latest pandemic protocols - Burns was injured running between wickets. He attempted to play through the pain but eventually retired hurt.
Scans confirmed a hamstring tear and while Burns will not require surgery, he has travelled to Brisbane to rehabilitate.
The Stars have already signed James Seymour as his replacement.
Marcus Stoinis tested positive to COVID-19 on game day last Tuesday as well and has fielded in neither of the Stars' games since, despite taking his place in the batting order.
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