But the Mail on Sunday reported he had been convinced to stay on until January.
The newspaper reported it was the introduction of Plan B coronavirus measures that prompted Lord Frost's decision, including the implementation of Covid passes.
It also said that he had become disillusioned by tax rises and the cost of net zero policies.
His resignation appeared to have blindsided Brexiteer MPs.
And it prompted Andrew Bridgen (North West Leicestershire) to warn Mr Johnson that he was “running out of time and out of friends to deliver on the promises and discipline of a true Conservative Government”.
He tweeted: “Lord Frost has made it clear, 100 Conservative backbenchers have made it clear, but most importantly so did the people of North Shropshire.”
Lord Frost has 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.
And his quitting piles more pressure on the PM, who has already suffered potentially his worst week politically since becoming Prime Minister with a giant backbench rebellion, the loss of a former Tory safe seat, and continued allegations over parties in Whitehall during lockdown restrictions.
In Northern Ireland, DUP leader Sir Jeffrey Donaldson his departure was a bad sign for Mr Johnson's commitment to removing the Irish Sea border.
Sir Jeffrey said: “This government is distracted by internal strife, and Lord Frost was being frustrated on a number of fronts.
“We wish David well. We enjoyed a strong relationship with him and his team, but this raises more serious questions for the Prime Minister and his approach to the NI Protocol.”
‘We deserve better than this buffoonery’ – Labour
Labour's deputy leader Angela Rayner said the news showed “a Government in total chaos right when the country faces an uncertain few weeks”.
She tweeted: “@BorisJohnson isn't up to the job. We deserve better than this buffoonery."
While Baroness Jenny Chapman, Lord Frost's opposite number for Labour, said: "The Government is in chaos. The country needs leadership not a lame duck PM who has lost the faith of his MPs and Cabinet.
“Boris Johnson needs to get a grip, tell us his plan for the next few weeks and bring certainty for the people of Northern Ireland by unblocking the stalemate over the Protocol.”
Liberal Democrat foreign affairs spokesperson Layla Moran said: “This shock resignation is a sign of the chaos and confusion at the heart of this Conservative government.
“The rats are fleeing Boris Johnson's sinking ship as he lurches from crisis to crisis.
“Even the Prime Minister's once-loyal supporters are now abandoning him, just as lifelong Conservative voters are switching in their droves to the Liberal Democrats.
“At a time we need strong leadership to get us through the pandemic, we instead have a weak Prime Minister who has lost the support of his allies and the trust of the British people.”