Her arrival was greeted by boos from Portuguese who want to loosen tight austerity measures imposed in exchange for a $99.2 billion bailout, The Financial Times reported.
Merkel is seen as the public face of the deal from the European Union, European Central Bank and the International Monetary Fund that has drawn criticism because of its high interest rate.
The chancellor plans separate meetings with President Anibal Cavaco Silva and Prime Minister Pedro Passos Coelho.
On Sunday, Merkel praised the country for its "courageous" deficit-reduction measures.
The center-left Socialists, headed by Antonio Jose Seguro, have said the country needs more time to consolidate accounts and pay debts.
In September, international lenders agreed to give Portugal one more year to meet its fiscal goals.
Portugal's economy minister, Alvaro Santos Pereira, has joined in the criticism, telling business leaders that Europe's bailout should not block "paths available to us for growth."
Merkel arrived in the country with a delegation of German businessman, saying she wanted to encourage more cooperation between Germany and Portugal that would create more jobs.
German investment in Portugal has fallen from 10.4 percent in 1996 to 3.3 percent in 2010.