Writing in The Times newspaper, George Osborne made the financial prediction as the Government continued to argue the case for staying in the 28-nation bloc.
He said the question facing British voters on 23 June is "one of the most fundamental our country has been asked to settle in a generation" and will have "profound consequences" for the UK economy.
Mr Osborne said the Treasury had carried out "rigorous analysis" of the long-term costs and benefits of EU membership or "Brexit".
He said leaving the EU would mean Britain would be "worse off, permanently so, and to the tune of £4,300 a year for every household".
He added: "The analysis shows that our membership of the EU, and the quota-free, no-tariff access it gives us to a single market of half a billion consumers, has increased our trade with our European neighbours by three-quarters.
"And increased our trade with the rest of the world too, because of the 50 or so EU free trade deals we are part of."
However, Vote Leave's John Redwood MP said the Treasury's analysis should not be trusted.
The Tory backbencher added: "The Prime Minister was one of the senior advisers working in the Treasury while John Major's government tried to keep this country in the EU's disastrous Exchange Rate Mechanism.
"The ERM destroyed jobs and caused misery for families across the country.
"The Remainers were wrong then, and they are wrong now - people should not trust their judgement on the EU."
London Mayor Boris Johnson, who is backing the leave campaign, has called for a Canadian-style, post-Brexit deal with Europe.
But Mr Osborne said that would cause Britain's economy to shrink by 6% by 2030, and questioned whether this is a "price worth paying".
He added: "The conclusion is clear: for Britain’s economy and for families, leaving the EU would be the most extraordinary self-inflicted wound."
Later today, Mr Osborne will publish more than 200 pages of analysis on EU membership and its alternatives.
The document will reportedly suggest there is no other model for a UK-EU relationship that gives quota-free, no-tariff access to a single market of 500 million consumers.
Mr Osborne's words will spark more accusations from Brexit campaigners that the Government is using scare tactics, and is doing Britain down by saying it cannot stand alone.
Last week, the Chancellor said homeowners could face higher mortgage costs in the event of an Out vote.