According to Buzzfeed, the leaked document, entitled EU Exit Analysis - Cross Whitehall Briefing and drawn up for the Department for Exiting the EU, suggests nearly every part of the economy would suffer.
The First Minister said: "When the Scottish Government published our own impartial analysis a few weeks ago, showing an extreme Brexit could cost each person in Scotland £2,300 a year, the Tories accused us of scaremongering - now we find out that behind the scenes they agreed with us".
The analysis, titled "EU Exit Analysis - Cross Whitehall Briefing" and dated January 2018, looked at three possible scenarios: a no-deal scenario, in which the United Kingdom would revert to World Trade Organization (WTO) rules, a comprehensive free-trade deal with the EU and a continued single-market access through a European Economic Area membership. In the best of the three scenarios, where Britain remains in the single market through membership of the European Economic Area, growth would still be lowered by 2% in the longer term.
Britain is due to exit the European Union on March 29, 2019, but there are deep divisions inside Prime Minister Theresa May's government and party about what sort of relationship should replace 46 years of membership.
"When we bring forward the vote on the final deal that we agree with the European Union, we will ensure that this House is presented with the appropriate analysis the Government has done so that the House can make an informed decision" he said.
The leaked secret study was meant to be shown confidentially to cabinet ministers this week.
Meanwhile Labour is to seek to force the Government to release its latest assessment of the impact of Brexit on the economy through a binding Commons vote.
"The real question, however, is how can a minister prepared to undermine the government he serves retain the confidence of the Prime Minister?"
Mr Baker told the Commons that civil service forecasts were "always wrong".
Sir Keir said: "We have been here before".
The report was leapt upon by government critics within and outside the Conservative Party. "Will he do so?"
He said Labour's strategy on Brexit was becoming clear for all to see - "demoralisation, delay and revocation".
Ken Clarke, Anna Soubry and Antoinette Sandbach were among at least 50 MPs to sign a cross-party letter from the APPG on EU Relations co-ordinated by pro-EU campaign Open Britain on Tuesday backing the move.
Official assessments which predict an economic hit from Brexit can not be dismissed, a Government minister has said.
"It's an incomplete report... deliberately leaked because it gives a bad view", he said.
And in comments that will fuel the internal Tory debate over Europe, Mr Rees-Mogg told Sky News that recent comments from Chancellor Hammond had been "very unhelpful" and he was "making himself a semi-detached member of the Cabinet".