It says much more needs to be done to tackle malnutrition in the world’s poorest countries.
The charity found that many families could not afford meat, milk or vegetables.
The survey covered families in India, Bangladesh, Peru, Pakistan and Nigeria.
One parent in six said their children were abandoning school to help out by working for food.
A third of parents surveyed said their children complained about not having enough to eat.
The survey was carried out in the five countries – where, the agency says, half the world’s malnourished children live – by international polling agency Globescan.
Record food prices
Save the Children said that a year of record food prices had worsened child malnutrition and could hit progress reducing child deaths.
“The world has made dramatic progress in reducing child deaths, down from 12 to 7.6 million, but this momentum will stall if we fail to tackle malnutrition,” said Save the Children chief executive Justin Forsyth.
The agency wants the UK to lead the way in reducing hunger and protecting children from food price rises – starting with a Hunger Summit when world leaders are in London for the Olympics.
The UK’s International Development Secretary, Andrew Mitchell, said the charity was right to focus on hunger and malnutrition, and Britain would “continue to urge other countries to match our own efforts in this area”.
In its report, Save the Children says that one in four of the world’s children have stunted growth – meaning their body and brain have failed to develop properly due to malnutrition.
Eighty percent of stunted children live in just four countries, the charity says.
Malnutrition contributes to the deaths of 2.6 million children each year, according to the report.
Assumpta Ndumi, a nutritionist who works with Save the Children in Kenya, told the BBC’s Network Africa programme that successive droughts are causing a downward spiral there:
“When another drought comes and livelihood assets are destroyed it becomes worse for families to be able to feed their children.
“Milk is very important for families in north-eastern Kenya, so when livestock is lost they basically have no access to a protein source.
“We need to address the hidden hunger because it’s killing silently.”
Food prices rose sharply in the first half of last year, according to the UN’s Food and Agriculture Organisation (FAO), after severe weather in some of the world’s biggest food exporting countries in 2010 damaged supplies.
The FAO’s Food Price Index rose last month for the first time since July 2011, but was still 7% lower than in January 2011.