The Mail on Sunday says he had concerns over stricter Covid curbs in England and recent tax rises.
Brexit minister Lord Frost has reportedly resigned from Boris Johnson’s government.
Lord Frost led the UK’s negotiations over the EU Withdrawal Agreement and Northern Ireland Protocol.
The Mail on Sunday, which first reported the news, said he handed Mr Johnson his resignation a week ago.
He resigned over the “political direction” of the government including the introduction of stricter Covid curbs in England, the paper said.
The Mail on Sunday said Lord Frost, who attended cabinet, would leave on good terms and had been persuaded to stay in his role until January.
It comes after a week where the prime minister suffered a by-election defeat with the Conservatives losing the previously safe seat of North Shropshire – which the party had held for nearly two centuries – to the Liberal Democrats.
He also endured the biggest rebellion of his premiership so far when many of his own MPs voted against the government over the introduction of so-called Plan B curbs in England.
A total of 99 Conservatives voted against the government, but the measures – including Covid passes at larger venues – passed by a majority of 243 thanks to Labour support.
Lord Frost had most recently been engaged in negotiations with the EU over post-Brexit arrangements.
This included elements of the Northern Ireland Protocol, agreed by the UK and EU in 2019, that allows goods to cross the border between Northern Ireland and the Republic of Ireland without checks.
The protocol has been criticised by some businesses for making it more difficult to send goods to Northern Ireland from Great Britain.
DUP leader Sir Jeffrey Donaldson said Lord Frost’s resignation raised questions about the UK’s approach to the Northern Ireland Protocol.
Sir Jeffrey said Mr Johnson “must now urgently decide which is more important – the Protocol or the stability of the political institutions”.
Northern Ireland’s deputy first minister, Sinn Fein’s Michelle O’Neill, said momentum was needed in negotiations to make the Protocol work better.
“The North will not be collateral damage in the Tory chaos,” she added.
What is the latest on post-Brexit talks?
Lord Frost had recently been locked in tense rounds of talks with European Commission vice-president Maros Sefcovic as the UK and the EU attempt to close gaps in post-Brexit arrangements.
On Friday, the UK government indicated the European Court of Justice could have a role in the Northern Ireland Protocol – a deal agreed between the UK and EU in 2019.
That could mean the court ruling on issues of EU law, but not having the final say in disputes over the protocol.
Indicating his frustration in a statement on Friday, Lord Frost said there had been some progress over solutions to outstanding issues “but not as much, and not as quickly as we had hoped”.
In what Lord Frost described as the “main area of progress”, the EU has said medicines will continue to be available in Northern Ireland at the same time as in the rest of the UK.
But he added: “Overall, with the potential exception of medicines, I do not believe that the negotiations are yet close to delivering outcomes which can genuinely solve the problems presented by the Protocol.”
He concluded by saying it was disappointing that a comprehensive or worthwhile agreement with the EU had not yet been reached and that a “solution needs to be found urgently early next year”.
Backbench Tory MP Andrew Bridgen said Mr Johnson was “running out of time and out of friends to deliver on the promises and discipline of a true Conservative government”.
“Lord Frost has made it clear, 100 Conservative backbenchers have made it clear, but most importantly so did the people of North Shropshire,” he wrote on Twitter.
Labour’s deputy leader Angela Rayner said the resignation suggested the government was “in total chaos right when the country faces an uncertain few weeks”.