The woman, named Shahida Shahid, was a math student from Manchester University and was out dining at the Almost Famous Burgers in the city on Friday.
She collapsed nearly half a mile from the restaurant in Great Northern Warehouse and died in hospital on Monday.
A police spokesperson said: "Initial inquiries have established the woman had been out for a meal in the Great Northern Warehouse prior to her collapse and may have suffered an allergic reaction to her food.
Marie Carter, company director of Almost Famous Burgers, said: "We are absolutely devastated to hear the tragic news that this young lady has passed away.
"As the authorities are conducting investigations it would be inappropriate to comment further at this stage.