Details from the dossier warn of food and medicine shortages if the UK leaves the EU without a deal.
Mr Gove, who is responsible for no-deal preparation, said the document was old and Brexit planning had accelerated since Boris Johnson became PM.
But he acknowledged no deal would bring disruption, or “bumps in the road”.
The leak comes as Mr Johnson is to meet European leaders later this week.
The prime minister will insist there must be a new Brexit deal when he holds talks with German Chancellor Angela Merkel and French President Emmanuel Macron.
According to Operation Yellowhammer, the dossier leaked to the Sunday Times, the UK could face months of disruption at its ports after a no-deal Brexit.
And plans to avoid a hard border between Northern Ireland and the Irish Republic are unlikely to prove sustainable, it adds.
The dossier says leaving the EU without a deal could lead to:
Fresh food becoming less available and prices rising
A hard Irish border after plans to avoid checks fail, sparking protests
Fuel becoming less available and 2,000 jobs being lost if the government sets petrol import tariffs to 0%, potentially causing two oil refineries to close
UK patients having to wait longer for medicines, including insulin and flu vaccines
A rise in public disorder and community tensions resulting from a shortage of food and drugs
Passengers being delayed at EU airports, Eurotunnel and Dover
Freight disruption at ports lasting up to three months, caused by customs checks, before traffic flow improves to 50-70% of the current rate
A No 10 source told the BBC the dossier had been leaked by a former minister in an attempt to influence discussions with EU leaders.
They added that the document “is from when ministers were blocking what needed to be done to get ready to leave and the funds were not available”.
Responding to the leak, Mr Gove said some of the concerns about a no-deal Brexit had been “exaggerated”.
He said: “It’s certainly the case that there will be bumps in the road, some element of disruption in the event of no-deal.
“But the document that has appeared in the Sunday Times was an attempt, in the past, to work out what the very, very worst situation would be so that we could take steps to mitigate that.
“And we have taken steps.”
Mr Gove also claimed some MPs were “frustrating” the government’s chances of securing a new deal with the EU.
He said: “Sadly, there are some in the House of Commons who think they can try to prevent us leaving on October 31st. And as long as they continue to try to make that argument, then that actually gives some heart to some in the European Union that we won’t leave on October 31st.
“The sooner that everyone recognises that we will leave on that day, the quicker we can move towards a good deal in everyone’s interests.”
Business minister Kwasi Kwarteng told Sky News’ Sophy Ridge on Sunday: “I think there’s a lot of scaremongering around and a lot of people are playing into project fear.”
But a former head of the civil service, Lord Kerslake – who described the document as “credible” – said the dossier “lays bare the scale of the risks we are facing with a no-deal Brexit in almost every area”.
“These risks are completely insane for this country to be taking and we have to explore every avenue to avoid them,” he told BBC Radio 4’s Broadcasting House.
Irish Deputy Prime Minister Simon Coveney said, in a tweet, that Dublin had “always been clear” a hard border in Ireland “must be avoided”.
The Irish backstop – the provision in former prime minister Theresa May’s withdrawal agreement that could see Northern Ireland continue to follow some of the same trade rules as the Republic of Ireland and the rest of the EU, thus preventing a hard border – was an “insurance policy” designed to protect the peace process, he said.
Michelle O’Neill, Sinn Fein’s deputy leader, accused Mr Johnson of treating the Northern Ireland peace process as a “commodity” in Brexit negotiations.
She said Ireland as a whole had been voicing concerns about a no-deal Brexit for months.
The SNP’s Stephen Gethins said the documents lay bare the “sheer havoc Scotland and the UK are hurtling towards”.
What is the Irish border backstop?
Liberal Democrat MP Tom Brake said they showed the effects of a no-deal Brexit should be taken more seriously.
“The government has simply, I think, pretended that this wasn’t an issue,” he said
Ministers were in “a real pickle” since the “the US has said that if that border is jeopardised, we’re not going to get a trade deal with them”, he added.
Speaker of the US House of Representatives Nancy Pelosi said on Wednesday that a US-UK trade deal would not get through Congress if Brexit undermined the Good Friday Agreement.