Mum Lisa Grantham says she was left humiliated when a security guard shouted: "You're barred – you and the kids", while she was at the checkout.
Her daughter Dulcie, five, was munching a chew bar she'd bought during an earlier trip to the store in Coventry, where she sometimes shops three times a day.
Lisa, 26, told her local paper: "I was chatting with the lady at the counter, we were laughing. The children were behaving themselves, then the security man came over.
"He said 'the kids shouldn't be eating in here'. I said that he knew I had bought that sweet earlier and he agreed.
"Then I said 'Are you trying to say I didn't buy them?' "He then shouted across the store: 'That's it, you're barred – you and the kids'.
"It came out of the blue and I felt so humiliated because the shop was busy. I was never made to feel so bad in my life.
"I've seen lots of children eating in there before – we've done nothing wrong."
Tesco admitted banning the family but say it was because the security guard believed the chew bar had not been paid for.
A spokesman said: "We understand that it can be difficult to keep an eye on small children while shopping but staff in the store have spoken to the customer before about incidents like this.
"We would of course be happy to reconsider the ban if we are given a reassurance that it won't happen again."