The four and five-year-old children from Devon were weighed and measured as part of the government's National Childhood Measurement Programme.
Parents of children at Tor Bridge Primary School contacted The Plymouth Herald about the letters.
Plymouth's director of public health Dr Ruth Harrell said support was in place for parents to discuss the results.
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School nurses working for Livewell South West sent out the letters as part of the Public Health England scheme.
Teri Sanders, mother of Archi Sanders who attends the school said: "According to the NHS guidelines, my son needed to be one stone lighter to be a perfect weight.
"I can understand why the NHS needs to warn parents or give a guideline, but I think it's disgusting that they can label my son very overweight."
Sarah Tall, whose four-year-old daughter Roxanne attends the school, put her child's details into an NHS healthy weight calculator, which confirmed the findings.
"She hasn't got an ounce of fat on her," Ms Tall said.
"My main worry is if a child is at an age where they can be very self conscious, it would affect them.
"If they're telling us our children are overweight, they should be a bit more sensitive."
The results are posted to parents and are not given to the children themselves or to the school.
Dr Ruth Harrell, Plymouth City Council's director of public health, said some parents might be "surprised" by their child's result.
"The measurement that we perform is our best estimate of the amount of excess weight that a child is carrying, but very occasionally might not be giving us the full picture."
Jake Franklin, aged five, was also classed as "very overweight", although his mother Kelly said it is "the least of his worries".
Jake underwent nine hours of brain surgery when he was a baby and has several learning difficulties.
Kelly said: "I didn't expect it to be written like that. I would like a formal apology for the way it was handled.
"I would also like to point out, it's nothing to do with the school, the school have a very healthy lifestyle policy".
Parents have said they are appalled by an "insensitive" letter describing their children as "very overweight".