Merkel, whose conservatives were weakened after they won an election in September with a reduced number of seats, said she would inform the German president that she could not form a coalition, after the pro-business Free Democrats withdrew from negotiations.
The development thrust Germany, Europe's biggest economy, into a political crisis that raised worries among investors of a new election if Merkel cannot form a minority government.
The news revived "a key risk factor" for the continental single currency, said Joe Manimbo, senior market analyst at Western Union Business Solutions in Washington.
"With the euro losing favor, given the messy can of worms that has been tipped over in Europe, that's helping the US dollar weather its own political uncertainties," he said.
The dollar index rose to 94.039, its highest since Nov. 14.
The greenback also climbed against the Japanese yen, rising to a session high of 112.40 yen in early North American trading as US stock markets opened higher and traders took risk-on positions, finding little favor in the safe-haven currency.
The euro fell to $1.1720 in overnight trading following news of the failure to form a coalition German government. It fell dramatically against the yen to 131.16 yen , its weakest since Sept. 15.
"There's a bit of uncertainty - we don't know what the next step is going to be, whether it's going to be a minority government or fresh elections - but in terms of the bigger picture I don't see any significant change in how you value the euro," said MUFG currency strategist Lee Hardman in London.
Hardman added that he thought the initial selloff that took the euro to its lows was exaggerated.
Bitcoin was trading at just above $8,100, after hitting a record high of $8,226 on the Luxembourg-based Bitstamp exchange on Sunday.
Many analysts expect this to be a relatively calm week of trading, with US markets closed for the Thanksgiving holiday on Thursday and with few major data releases.
Traders will be awaiting a speech by Federal Reserve Chair Janet Yellen late Tuesday and a release Wednesday of minutes from the Fed's November meeting for clues on the direction of US monetary policy.