A 55-year-old man, who is known to the female, has since been arrested on suspicion of attempted murder.
He remains in police custody at this time.
Emergency services were called to reports of a stabbing at 13:30 this afternoon at Morrisons, Castle Quay in St Helier.
The area currently remains cordoned off.
A large number of emergency service vehicles could be seen lining the road outside the shop this afternoon.
Police would now like to speak to anyone who may have seen the incident or who has any information.
You can call police on 612612, or the independent charity Crimestoppers anonymously on 0800 555 111 or online at Crimestoppers-uk.org.
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