The Italian premier's crushing defeat and resignation came as a personal blow to Merkel, who has had an excellent relationship with the former mayor of Florence since he came to power in February 2014.
Foreign Minister Frank-Walter Steinmeier said on Monday that Germany was “concerned” by the result.
"We are watching the result in Italy with concern," Steinmeier, who is visiting Greece, told Greek Prime Minister Alexis Tsipras in televised remarks.
"I think Renzi did the right thing, the necessary thing, but voters did not support him," he said through a translator.
"This is not of course a state crisis, but it's a government crisis that needs to be resolved... it's not a positive message to Europe at a difficult time," he added.
Italians voted on Sunday against proposed reforms that would have curtailed the size and powers of the Senate and transferred powers from regions to the national government.
Opposition parties had denounced the proposed amendments to the constitution as dangerous for democracy because they would have removed important checks and balances on executive power.
Italian interior ministry projections suggested the No camp, led by the populist Five Star Movement, had been backed by 59.5 percent of those who voted.
'A slap on the wrist for the establishment'
Italy's president, Sergio Mattarella, is widely expected to call for the creation of a transitional technocratic government. But with the Five Star Movement polling strongly, new elections in the longer term could see the country entering uncharted territory, far from the relative stability Merkel welcomed in Renzi.
Analysts have cautioned against viewing the Italian referendum solely through the prism of populism - even seasoned members of Renzi's own Democratic Party, such as former Prime Minister Mario Monti, appealed for a No vote.
But the anti-immigrant Alternative for Germany (AfD) was quick to interpret the result as an anti-establishment rallying cry. Alice Weidel, a leading figure in the AfD, said the result was “a slap on the wrist for the establishment from the ordinary people, who are deeply dissatisfied with their state.”
Prime Minister Renzi and the European Central Bank (ECB) had both failed Italy's squeezed middle class, she claimed.
The ECB's “catastrophic monetary policy” had made Italy a “second Greece”, said Weidel.
She called on Italy to leave the eurozone - a move the Five Star Movement has pledged to push for if it takes power.
Reasons to be cheerful?
But Carsten Brzeski, chief economist with ING-Diba bank, played down the significance of the vote.
“Toppled governments in Italy are really nothing new, and Europe has already survived a lot,” he said on Monday. He also saw in Renzi's defeat an opportunity for Italy.
“A technocratic transitional government can join forces with Europe to tackle the problems in the banking sector and the reform backlog with greater abandon than the Renzi government,” he added.
'Like Cameron, Renzi gambled too high'
His optimism was not shared by Helaba bank's chief economist Gertrud Traud, who saw the outcome as a blow to the euro and Italy's government bonds. If the result sparks major turbulence on financial markets the ECB will have to intervene, she said.
“Like Cameron, Renzi gambled too high,” she said. Like Italy's premier, the former British Prime Minister David Cameron too staked his future on a popular vote.
At Commerzbank, chief economist Jörg Krämer saw the result as a missed opportunity for Italy.
“Italy remains a crisis candidate,” he said on Monday.
“The risk of a Five Star Movement government and a return to the debt crisis is not off the table.”
Euro nears parity with dollar
The euro sank to a 20-month low on Monday and most Asian stocks also retreated as a fresh wave of uncertainty washed across markets after Renzi's resignation and heavy referendum defeat.
Analysts warned the single currency could soon hit parity with the dollar as investors are spooked by a long-running banking crisis in Italy and the possibility of elections that could usher in anti-EU parties.