Jeremy Corbyn said his party would introduce a VAT charge on private school fees to pay for the policy, which it hopes will raise £1.5bn a year.
Currently all children in reception class and years 1 and 2 receive free school meals in England, as well as those whose parents receive certain benefits.
Research released by the party suggests extending funding for free school meals to all primary school children would cost between £700m and £900m.
Labour's shadow education secretary Angela Rayner said cuts to school budgets introduced by the current government were impacting schools' ability to feed children, which was affecting pupils' health and attainment.
A National Centre for Social Research and the Institute for Fiscal Studies report has shown offering universal access to free school meals improves educational attainment, enabling primary school children to advance by an average of two months.
"While the Conservatives offer tax giveaways to their billionaire friends, they are cutting the schools budget and threatening the health and futures of all our children by denying children the basic right of a healthy lunch at school," said Rayner.
"By investing in our education system and providing free school meals for every primary school child, we will remove the stigma attached to free school meals, and improve health and attainment for all children."
Former Ofsted chief inspector Sir Michael Wilshaw backed the idea of putting VAT on private school fees, saying the independent sector should do more to support mainstream schools.
However, speaking on BBC Radio Four's Today Programme, he said Labour's proposed policy would result in families who did not need subsidies benefiting unnecessarily, and that the money would be better directed towards funding initiatives such as the pupil premium.
"I would rather see any extra cash that is available being given to poor parents," he said.
"What we have seen over the last few years is that the pupil premium has worked.
"It has worked particularly in primary schools where the attainment gap between free school meal children and non free school meal children has narrowed, and narrowed quite considerably."
Julie Robinson, general secretary of the Independent Schools Council, criticised the plans, saying the policy would be "counterproductive".
"A third of pupils at our schools are on reduced fees and are from families where both parents work hard to pay the fees," she said.
"If this measure was introduced, smaller independent schools may close, driving more children back to be funded in the state system.
"Half a million children are educated in independent schools, saving the state £3bn."
Labour's figures for the amount of money the VAT charge could raise was based on estimates made by The Fabian Society in 2010.
The next general election currently scheduled to be held in 2020.