Merkel and Rajoy postponed their joint press conference in the face of protests in the capital of Spain's Galicia region, Spain's El Público newspaper reported.
Scuffles broke out as police tried to prevent people from entering Santiago's Plaza de la Quintana square, after being turned away from the city's Plaza del Obradoiro, outside the city's cathedral.
Several people were pushed to the ground in the face of police charges, Spain's 20 minutos newspaper reported.
Police called for back-up as demonstrators moved forward, the daily added.
"We want work. We don't want to emigrate," some of the demonstrators were heard to yell out, while others called for Merkel and Rajoy to leave Galicia.
Several people were injured in the scuffles, but local government officials justified the police response, saying the demonstration was illegal as police had not been notified.
A pesares do cordón policia, a verdadeira faciana de Merkel e Rajoy chegou á Quintana. Non nos calarán! Fóra a Troika pic.twitter.com/qhicPs5rGu
— Rubén Cela (@rubencela) August 25, 2014
On Sunday, the two leaders walked along the pilgrimage road to Santiago de Compostela on Sunday under bright sun in a symbolic show of unity with Spain and its arduous path to economic recovery, but not all Spaniards were delighted with her presence.
Merkel, 60, joined Spanish Prime Minister Mariano Rajoy on the route as she prepared for a European Union summit on Saturday to decide who gets the top jobs in the 28-nation bloc for the next five years.
— La Voz de Galicia (@lavozdegalicia) August 25, 2014
The two leaders took about an hour to walk a six-kilometre (3.7-mile) stretch of the pilgrimage trail between the villages of O Pedrouzo and Lavacolla, near the airport at Santiago de Compostela.
Merkel, who wore white trousers and a white shirt, and Rajoy, 59, who was casually dressed in jeans and a blue shirt, talked as they walked at a brisk pace escorted by bodyguards.
Her two-day visit to the northwestern city of Santiago de Compostela coincides with signs of a gradual, yet jobs-scarce economy recovery in Spain since it emerged from recession in mid-2013.
Viewed just two years as the wobbly financial domino of the eurozone, Spain is now heralded by some as a showcase of economic reform and budget restraint, despite its 24-percent jobless rate.
Indeed, Spain's 54-year-old economy minister, Luis de Guindos, is being touted as the next head of the Eurogroup, forum of the finance ministers of the single currency zone.
Rajoy's former agriculture minister, Miguel Arias Canete, 64, is also being tipped to be the new commissioner for agriculture and rural development.
Other key posts at the European Commission, which proposes and enforces laws for 500 million Europeans, include the commissioners in charge of trade, energy policy and competition.
Not everyone in Santiago de Compostela was happy about the presence of the pro-austerity German chancellor. She was jeered and booed outside her hotel with people shouting "Down with the Troika!".
— Onda Cero (@ondacero) August 25, 2014
The Spanish and German leaders will hold a news conference on Monday before visiting Santiago de Compostela's cathedral, the reputed burial place of Saint James, one of the twelve apostles of Jesus Christ.
The pilgrimage known as the Camino de Santiago, Spanish for the Way of Saint James, has existed for more than 1,000 years.
The most travelled among several ancient routes leading to Santiago de Compostela is the Camino Frances, nearly 800 kilometres (500 miles) long.
It starts from the French side of the Pyrenees mountains and leads to Santiago de Compostela.
Thousands of people from around the world walk part of the trail every year. Many carry wooden walking sticks adorned with the distinctive scallop shells that symbolize the pilgrimage.
Growing numbers of people set out on the trail for reasons other than religion, attracted by the beauty of the landscapes, the medieval sights, or the physical challenge.