Steve Webb said that around 100,000 to 200,000 annuity sales could still take place every year and said these products are likely to become more competitive as providers will know that retirees have a greater choice of options available to them.
He made the comments as Standard Life reported that its UK annuity sales halved in the weeks after the Budget.
Mr Webb was appearing before the Work and Pensions Committee to answer questions on the retirement shake-up announced in the Budget, which has relaxed rules in order to give people more control over what they do with their money when they retire.
The reforms are expected to lead to fewer people using their pension savings to buy an annuity when they retire, which gives them a fixed income, usually for life.
Controversy over annuities has been growing amid tumbling rates in recent years and concerns that people are not getting the best deal they could by shopping around. Up until now, around 400,000 people a year have bought an annuity.
Mr Webb said of the shake-up: "I don't think it is a death blow to annuities. Clearly there is a set of people, and we can argue and discuss how large that will be, who won't buy annuities now, and estimates, and they are only guesstimates really, vary considerably.
"But clearly an awful lot of people still need an income in retirement."
Mr Webb said: "It depends who you listen to, but it's still thought 100,000, 200,000 annuities a year will be sold... I don't think that the process is irredeemable."
But he continued: "Annuity providers will now know that people have got a realistic choice, which is not buying, just taking some cash and investing somewhere else.
"And I think that will shake up the market in a way that an incremental reform wouldn't have done. I don't think annuities are inherently a bad product. But we clearly need the market to work better."
He said some people will end up buying an annuity later and some may choose to buy a smaller annuity than they might otherwise have done.
He said: "I think there will be a range of responses... there will still be plenty of people buying annuities and other financial products of a similar nature."
Mr Webb made the comments as Standard Life reported that changes to annuity regulations had resulted in its UK annuity sales plunging by around 50% following the Budget announcement.
It said: "While it will be some time before long-term trends become clear, the negative profit impact of the changes will reflect the relatively small size of our annuity business."
Standard Life said it has seen a trend of people simply cashing in pension pots worth less than £10,000, while those with bigger pots have been deferring their plans. Annuities contributed £45 million to its overall operating profits of £750 million last year.
Last month, Legal & General predicted that the whole annuities market is set to shrink to around one quarter of its current size, which would see it plummet from being worth £11.9 billion last year to £2.8 billion in 2015.
Some of the changes announced in the Budget have already come into force. They mean that amount of overall pension wealth that someone aged over 60 can take as a lump sum has almost doubled from £18,000 to £30,000.
The size of a small pension pot that someone can take as a lump sum, regardless of their total pension wealth, has increased five-fold, from £2,000 to £10,000.
From April 2015, someone aged over 55 will be taxed at their normal marginal rate if they want to access their pension money, which will be 20% for most people, rather than the "punitive" rate of 55% for withdrawing the pot now.
Asked if he was concerned that businesses would be put off by surprises like those unveiled in the Budget, Mr Webb said there is a tradition of Budget secrecy for "good reason", adding: "Sometimes you have to make big, bold decisions."
The changes will also give people access to free, impartial guidance to help them decide what to do with their pension savings and the Government is currently working on fleshing out the details of what this should include. Some £20 million has been put aside to get the guidance up and running.
Mr Webb said emphasised that what is being offered will be guidance rather than independent financial advice. He said the guidance will be to a requisite standard and content and the Government has been discussing the plans with advice bodies like the Money Advice Service (MAS).
He said people will have an entitlement to speak to someone face to face, but this will not be forced on them.
Mr Webb also recently suggested that people should be given an idea of when they might die in order to help them plan their finances for retirement.
He told the committee that this could involve giving people scenarios for how long they might expect to live for, adding that he is not suggesting people will be told "with any precision" exactly when they might die.