Kwasi Kwarteng also suggested the VAT cut for hospitality firms would continue "while lockdown persists". The reduction – 5 per cent – rate of VAT for the hospitality sector is also due to end on March 31.
Asked on BBC Breakfast if the job support scheme would be extended, Mr Kwarteng said: "I think the Chancellor has already indicated that we will be extending furlough.
"I think that has been part of a public announcement. I think there will be other measures that we will see tomorrow."
Mr Kwarteng told BBC Radio 4's Today it was a "fairly good assumption that while lockdown persists there will be additional support".
"I think it is really important that we don't crush the recovery before it's happened," he said.
"In order to keep people's jobs going, in order to keep companies going we need to continue providing support. I think there is every indication that is what the Chancellor will do.
"My view is that the way to get out of this difficult situation is to grow the economy."
Covid restrictions are set to end by June at the earliest in England, with the route map out of lockdown for Scotland yet to be announced beyond April 26.
Chancellor Rishi Sunak will focus on "critical support" for businesses and households in his Budget rather than immediate efforts to balance the books, Mr Kwarteng said.
The Chancellor has said his address to MPs on Wednesday will be characterised by "honesty and fairness", indicating he will set out how he intends to begin the task of repairing the public finances which have been battered by coronavirus.
Mr Kwarteng played down the prospect of immediate large tax increases, but said Mr Sunak had acknowledged the country could not "go on spending money forever".
"For now, what we have to do is support businesses, individuals, families, through what has been an extremely difficult time," he told BBC Breakfast.
"We have got another three years to run in the parliament and the Chancellor will be looking to reduce the deficit.
"For now, I think the real emphasis is on trying to provide critical support."
If the vaccine rollout proceeds successfully and the economy is reopened by June 21 – as envisaged in England's road map – then "there is every chance that the economy can bounce back, we can see strong growth at the end of 2021 and that will be the best way to deal with the growing deficit", Mr Kwarteng said.
But former Tory leader Lord Hague – an ally of Mr Sunak, who succeeded him as MP in Richmond, north Yorkshire – bluntly warned that taxes would have to go up to pay for the cost of coronavirus.
That could result in a clash with Tory MPs who want a low-tax economy and find themselves in alliance with Labour leader Sir Keir Starmer, who has warned that now is not the time to increase levies on businesses and families.
The Office for Budget Responsibility (OBR) will publish its latest forecasts alongside the Budget on Wednesday, with Prime Minister Boris Johnson expecting a recovery to be "much stronger than many of the pessimists have been saying".