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 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."