The party said 40,000 primary age children were taught in classes of 36 or more in England in 2016, blaming "broken promises" by the government.
But the Tories said Labour's attacks were "a massive own goal".
They said the Labour-led Welsh government had overseen increases in class sizes in Wales.
Mr Corbyn, who insisted on Thursday that he could defy the polls and "change the direction" of the election, has used Labour analysis of Department for Education figures to focus on education.
He said: "The prime minister herself has said that super-sized classes are proof of a school system in a crisis.
"And that's what we've got on the Tories' watch.
"School leaders and teachers have said Tory cuts to school budgets will mean class sizes will be forced to grow even larger. We cannot risk our children's education in this way."
In his speech, Mr Corbyn appeared to confuse some of the statistics released earlier by his party, inadvertently overstating the number of children in large classes.
He told supporters: "500,000 children in England - half a million children - are now being taught in super-sized classes of over 36".
The half a million figure is for class sizes of 31 - 34. A Labour spokesman said Mr Corbyn had mixed the figures up.
A Conservative spokeswoman dismissed Mr Corbyn's comments and pointed out that the number of infants in large classes had risen by 18% in three years in Wales.
"Of course we are not complacent about the situation in England," she added.
"There is more to do and that's why we are spending a record amount on schools - something we can afford to do because of our careful management of the nation's finances."
Elsewhere on the campaign trail on Friday, Mr Farron will challenge Tory MPs who supported staying in the EU to oppose a so-called hard Brexit.
He will add: "If these Tory MPs reject these principles and back a hard Brexit manifesto, then people will know that on the biggest issue of the day they went missing in action."
Chalk and cheese. Black and white. Night and day. Yin and yang.
Theresa May and Jeremy Corbyn are not, repeat not, cut from the same cloth. Their fundamental beliefs differ enormously. Their solutions for society's problems are poles apart.
Politicians in opposing parties are sometimes friends across the boundaries. But it is hard, extremely hard, to imagine the Labour leader and the Tory leader ever quietly enjoying a pootle round the Berkshire countryside of a weekend, or a cappuccino in Islington in a quiet moment.
But right at the start of this election - whisper it - there is something significant they share.
Read Laura's blog in full
Labour says children are being crammed "like sardines" into "super-sized" school classes, as it focuses its general election campaign on education.