The business secretary announced in the House of Lords that the state of the economy had made it "impossible" to complete a deal on favourable terms.
"When market conditions change we will return to the issue," he told peers.
The partial sell-off, opposed by many Labour MPs, had been due to go before Parliament before the summer break.
'Impossible to conclude'
Lord Mandelson said that the government remained convinced that selling off part of the Royal Mail was the best way forward.
But under current market conditions it would be "impossible to conclude" the process in a manner which would "secure value for the taxpayer", he added.
"We have thoroughly tested the market to see who is interested in partnership, but economic circumstances, I need hardly point out, are extremely difficult," Lord Mandelson told fellow peers.
He continued: "I have always been clear that we would only do a deal with the private sector if it represented value for money for the taxpayer."
Ministers say private sector money needs to be brought in to help rescue the Royal Mail as it faces a pension deficit estimated at up to £8bn.
For the Conservatives, Lord Hunt of the Wirral said that by putting the Postal Services Bill into "cold storage" to suit "short-term political ends", the government was leaving the Royal Mail pension plan in an "impossible position".
Lord Mandelson replied: "This remains a matter for the company and the pension trustees."
Former postman and Labour peer Lord Clarke of Hampstead said Royal Mail workers and management were "living without certainty" because of the pension deficit.
Lord Cotter of the Lib Dems said the government was "collapsing from the position" it put forward in support of the bill.
But a spokesman for the prime minister said the government would "return to the issue when market conditions change".
Billy Hayes, general secretary of the CWU union, which was strongly opposed to the proposal, said the government had "not only looked at market forces but has listened to the British public".
BBC political correspondent Laura Kuenssberg said the government was understood to have had difficult finding a business that would buy part of the Royal Mail.
The business secretary said on Monday that the bill was being "jostled for space" among other legislation ministers wanted to conclude before Parliament breaks for the summer.
Lord Mandelson said on Monday that the partial sell-off would not happen until "later", but the Lords statement is the first time he has confirmed that the part sale will definitely not go ahead in the near future.
There has been growing speculation that the partial sell-off, which is controversial within the Labour Party, will not go ahead before the next election.
More than 140 Labour backbenchers had signed a Commons motion critical of the plan and there had been rumours for weeks that the scheme could be shelved.