The superstore, in Savile Street, was evacuated just after 1.30pm after a man attacked two people with a screwdriver, leaving them with serious injuries.
One shopper, who was in the store at the time of the attack, said that one of the victims was near the baking section when she was stabbed.
They said: “All I saw was a woman screaming with blood all over her and the security guards were running towards us.
“The lady was down near the baking bit where all the bread is in the bottom right corner. I saw was a woman start screaming then security chasing someone.
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“We were all told to leave about five minutes after it happend. I didn't see the other victim but I'm guessing that’s what all the commotion was in the staff only part. We just heard loads of shouting.”
Customers were evacuated from the store which is currently on lockdown following the attack.
A South Yorkshire Police spokesman said: “It was reported that a man and a woman had been assaulted by a man carrying a screwdriver outside of the Tesco store.
“Both have been taken to hospital for treatment. Their injuries are described as serious.
“A man has been detained at the scene and remains in police custody.
“There is a large police presence in the area at present and the store has been evacuated as officers carry out enquiries and examine CCTV footage.”