Failure to bridge a multi-billion euro valuation gap between the parties leaves Italy unable to complete the restructuring of its banking system which it started six years ago.
The announcement confirmed what Reuters had exclusively reported from sources on Saturday.
Rome will now seek an extension of deadlines agreed with European Union authorities to re-privatise MPS and a Treasury official said it did not expect discussions to be difficult.
The Treasury will do its part to recapitalise MPS and plans to go ahead with the measures to improve the balance sheet which it had offered to UniCredit after MPS emerged as the most vulnerable euro zone lender in this summer's health check of the sector.
"The postponement will be accompanied by managerial measures that will strengthen the bank," the official said.
"European authorities are fully aware that we have seriously tried to conclude a transaction at market terms within the end of the year, and that this has not been possible, because the proposal we have received is not acceptable," he added.
Italy had started working towards re-privatising MPS not long after rescuing it in 2017 for 5.4 billion euros ($6.3 billion), proceeding as a first step to rid of most of its remaining soured debts.
Rome saw a merger with a stronger peer as the best way to fix the country's biggest banking woes and had singled out UniCredit after rival heavyweight Intesa Sanpaolo pushed its market share to antitrust limits with last year's UBI takeover.
"Despite the effort from both sides ... the negotiations pertaining to the potential acquisition of a defined perimeter of Banca Monte dei Paschi di Siena will no longer continue," UniCredit and the Treasury said in a joint statement.
The news is likely to rock shares in the two banks on Monday and hit in particular MPS' riskier debt, which has suffered in recent months due to worries MPS' junior bondholders will be called to bear losses under European Union rules on state aid for banks if Italy puts more taxpayer money into MPS.
Early discussions to cut the state's 64% stake in MPS through a deal with UniCredit started more than a year ago, but the ousting of CEO Jean Pierre Mustier brought them to an abrupt halt.
In agreeing to enter exclusive talks with the Treasury in July, new UniCredit Chief Executive Andrea Orcel demanded the deal targeted only parts of MPS, in addition to being neutral for UniCredit's capital and offering a 10% earnings boost.
The Treasury calculated the assets selected by UniCredit had a market value of between 3.6 billion and 4.8 billion euros given 600 million euros in annual net income, a person with knowledge of the matter said.
That opened a yawning gap with UniCredit's 1.3 billion euro valuation of the same assets, the source added. UniCredit declined to comment.
The Treasury also opposed accounting adjustments UniCredit had factored into its 6.3 billion euro capital request on the basis of its own more conservative risk models, sources have said.
With the parties at odds also over the assets to be sold and the Treasury pushing UniCredit to take on MPS units it did not want, Rome concluded a merger was too costly an alternative for taxpayers.
MPS has plans to raise 2.5 billion euros in capital if it failed to find a buyer and the Treasury official said the government was ready to do its part on the basis of "a credible business plan".
Italy is likely to overhaul MPS' leadership to deliver the scheme devised as part of the UniCredi deal, which would see the bank's remaining soured loans transferred to state-owned bad loan manager AMCO and its legal risks carved out and guaranteed by the state, this source said.
The European Central Bank (ECB), which is yet to see a standalone plan according to a source close to the matter, has no immediate concern over MPS' capital position.
($1 = 0.8593 euros)
(Reporting by Valentina Za and Giulio Piovaccari in Milan, Giuseppe Fonte in Rome; editing by David Evans)
By Valentina Za, Giuseppe Fonte and Giulio Piovaccari