The ex-University of Pretoria man tore a muscle in Pirates' 1-0 victory over Polokwane City in the Premiership on Wednesday night.
Club doctor Thabiso Mmoledi confirmed Jali will need surgery after the player underwent a scan on Friday.
"Jali cannot play with the injury he is carrying. He has a bad tear on the muscle on his shoulder which will require an operation," Mmoledi told the Sea Robbers' official website.
"He will see an orthopaedic surgeon this week for the operation on his shoulder. It should take him up to six weeks to recover."
Lehlogonolo Masalesa, who has impressed in Jali's absence when called upon, is now likely to partner Oupa Manyisa in central midfield in Sunday's CAF Champions League clash with Al Ahly at Orlando Stadium.
Thandani Ntshumayelo has recovered from a lengthy ankle problem, but is still short of match fitness.
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