Hutchings, competing for the seat left vacant by disgraced Lib Dem Chris Huhne, said she believed it would be "impossible in the state system" for her son to get a good enough education to become a surgeon.
According to the Daily Mirror, Hutchings said on Friday: "William [her son] is very gifted which gives us another interesting challenge in finding the right sort of education for him – impossible in the state system. He wants to be a cardio-respiratory surgeon.”
However, the most recent Ofsted reports for a number of Eastleigh schools, including Thornden, Wildern and Toynbee high schools, have found them to be "outstanding".
Maria Hutchings received campaign support from David Cameron this week
Hutchings, a mother of four children, Victoria, 24, John Paul, 18, William, 12 and ten-year-old Harriet, was accused of being "out of touch" by opposition candidates for her remarks.
In response, the satirist John O'Farrell, standing for Labour in Thursday's byelection, said: “Ten years ago, when I was concerned about the lack of suitable local schools, I organised with other parents to set up a new non-selective state school.
“My own children went there and I served as chair of governors for eight years. Maria Hutchings claims to ‘get things done’ – but in actual fact the opposite is true. All she’s shown is that she’s just as out of touch as the rest of the Conservative party, whether on education, tax cuts for millionaires or trebling tuition fees.”
The Liberal Democrat leader of Eastleigh Borough Council Keith House said: "Although it's down to every parent to choose the right school for their child, it's simply not true to say that the education in Eastleigh is not good enough for our children.
"Ofsted have rated several local schools 'excellent', they were good enough for Liberal Democrat candidate Mike Thornton's daughter to study medicine at Imperial College London, and they are good enough for the majority of Eastleigh parents who are proud to have such excellent schools to choose from.
"Maria's claim that it's 'impossible' to get a good state education in Eastleigh is an insult to the teachers who work hard to give our children the best start, and to the parents who are glad to have such good schools that are part of the local community."
A Conservative spokesman said: "Maria Hutchings wants all children to get the best possible education - that's why she's backing Michael Gove's reforms to bring back rigour to the state education system after 13 years of Labour.
"Maria has campaigned tirelessly to help parents of children with special educational needs get the best education for them."
The ill-advised comments from Hutchings follow embarrassing suggestions she copied parts of her website from online encyclopedia Wikipedia.
Elsewhere, Hutchings, who already stood for the seat in the 2010 General Election, was also spotted by Sunday Times journalist Kate Mansey hugging a woman asking for directions, mistaking her for a supporter. Mansey tweeted:
Hutchings, O'Farrell and Lib Dem candidate Mike Thornton will contend for the seat vacated by Chris Huhne after he admitted a charge of perverting the course of justice by persuading his wife Vicky Pryce to take the blame for his speeding offence in 2003.