It has emerged that some of the sauces, launched earlier this year, contain so much salt they would not be allowed to be served to primary school children.
Nutritional experts have confirmed that a four-year-old eating a quarter of a jar would have exceeded their recommended salt intake in one go.
Oliver's spicy olive, garlic and tomato sauce is produced in Italy and contains 3g of salt per 100g - up to six times as much as some rival products and twice as much as the equivalent weight of Turkey twizzlers.
According to the label on the jar, an adult eating half a jar would consume 88 per cent of their recommended daily salt allowance - the same as a heaped teaspoon.
It was revealed that other products in the range also have significantly higher salt contents.
Graham MacGregor, professor of cardiovascular medicine at St George's Hospital in south London , said he was alarmed by the findings.
"Jamie Oliver is very respected by the public, particularly for his work on healthy eating in children," he said.
"It is, therefore, deeply disappointing that he appears to be unaware of the dangers of eating too much salt. It's important because both children and adults who eat large quantities of these types of foods are much more likely to develop high blood pressure later in life and suffer unnecessary strokes and heart attacks."
Dr MacGregor, who also chairs the Consensus Action on Salt and Health, said Oliver's tomato, olive and garlic sauce contained 20 per cent more salt than Atlantic seawater.
A spokesman for Oliver denied the chef had let parents down.
He said: "Jamie spent a lot of time working on these sauces and they are designed to be eaten in the Italian way - one jar with at least 500g of pasta - feeding four to six people.
"Because they are more concentrated than rivals you don't need as much - and the salt content is dissipated. We are now looking at changing out labelling to make this clearer to consumers. A little of Jamie's sauce goes a long way."
