Police were called to the supermarket at around 1.30pm on Saturday to reports of an incident in Castle Quay, St Helier on Saturday.
They found a woman, 34, who had suffered stab wounds. She was treated by paramedics at the scene and taken to hospital for further medical assistance. Her condition is described as critical but stable.
It was not clear whether the assailant also worked at Morrisons or whether he entered the store as a customer.
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A 55 year-old man has been charged with attempted murder and is due to appear in magistrates court on Monday morning.
Jersey Police said there was no wider risk to the public. A police cordon was erected where the stabbing took place as forensic officers combed the crime scene for evidence.
Morrisons was closed after the stabbing and stayed shut on Sunday.
“Officers were called to reports of a stabbing at 1.30pm this afternoon at Morrisons, Castle Quay, in St Helier.
“A 34-year-old female had been stabbed multiple times by a man who left the scene.
“She was taken to the Emergency Department by ambulance and remains there in a serious condition.
“A 55-year-old man who is known to the female has since been arrested on suspicion of attempted murder and he remains in police custody at this time.
“Police would like to speak to anyone who may have seen this or who has any information.
“They can call police on 612612 or the independent charity Crimestoppers anonymously on 0800 555 111 or via their anonymous online form at Crimestoppers-uk.org”.
Morrisons has been contacted for comment.