Germany now faces weeks, if not months of paralysis with a lame-duck government that is unlikely to take bold policy action.
With no other viable coalition in sight, Germany may be forced to hold new elections that risk being as inconclusive as September's polls.
Merkel, whose liberal refugee policy has proved deeply divisive, had been forced to seek an alliance with an unlikely group of parties after the ballot left her without a majority.
"It is better not to govern than to govern badly," he said, adding that the parties did not share "a common vision on modernising" Germany.
Voicing regret for the FDP's decision, Merkel vowed to steer Germany through the crisis.
"As chancellor... I will do everything to ensure that this country comes out well through this difficult time," she said.
The euro fell following the news, although analysts said the longer-term implications for the currency were not yet clear.
The negotiations, which turned increasingly acrimonious, stumbled on a series of issues including immigration policy.
Merkel's liberal refugee policy that let in more than one million asylum seekers since 2015 had also pushed some voters to the far-right AfD, which captured 12.6 percent of the vote after an Islamophobic and anti-immigration campaign.
Party chiefs had initially set a deadline of 6:00 pm on Sunday, but that passed without a breakthrough -- after already blowing through a previous target on Thursday.
The Greens angrily deplored the collapse of talks, saying they had believed a deal could be done despite the differences and accusing the FDP of negotiating in bad faith.
Lindner, who had taken a harder line on refugees as the talks progressed, "opted for his kind of populist agitation instead of political responsibility", Greens Europe MP Reinhard Buetikofer tweeted.
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