The man, in his 20s, was n the Newport store with the snake, which was described as thin and dark-coloured.
Ursula Berry, 72, said she initially thought it was fake, but was terrified when she realised it was live.
A Tesco spokeswoman said the man was escorted from the store last Saturday, after he had paid for his shopping.
Mrs Berry, from Pontfaen, Newport, who shops regularly at the store in Spytty Road, said other people in the aisles were also shocked.
She said one young man asked the shopper about the snake.
“He told the young man that the snake was fed mice,” she said..
‘Started moving’
She said: “I thought it was fake at first but when the head and tail started moving I was terrified.
“Start Quote
He told the young man that the snake was fed mice”
End Quote Ursula Berry Shopper
“I couldn’t believe he was just able to walk into the supermarket. It’s not hygenic.”
Mrs Berry said she alerted a Tesco staff member, but the man walked off after he was first approached.
She said: “The lady from Tesco then went to call security and the last I saw of him was at the self-service checkouts.”
She said the young man had coloured hair and was weating a T-shirt with the snake wrapped around his arm.
A Tesco spokeswoman said he was escorted from the premises as soon as the snake was noticed.
She said: “The man was immediately stopped as soon as the snake was noticed.
“Staff scanned his items through the self-service checkouts for him, after which he left the store.”
Mrs Berry said the incident had had a lasting impact.
“I’ll never shop there again,” she said.