The comments by Horst Seehofer, chairman of the Christian Social Union (CSU) and state premier of Bavaria, exacerbated a rift within Merkel's camp over how to approach immigration and Islam that is gnawing away at her leadership.
"We don't need more immigrants from alien cultures," Seehofer told news weekly Focus, adding that Turkish and Arab immigrants often had difficulty integrating into Germany.
Opposition politicians branded the remarks incendiary and they also drew criticism from a leader of Merkel's Christian Democrats (CDU), senior sister party to the CSU.
Seehofer timed his outburst to coincide with Merkel's meeting with Turkish Prime Minister Recep Tayyip Erdoğan on Saturday, added fuel to an integration debate first sparked by former central banker Thilo Sarrazin's criticisms of Muslims.
"I don't have any sympathy for demands to allow more immigration from alien cultures," said the CSU chief, whose party has faced a steady erosion of support in opinion polls.
"The multi-cultural society is dead," he told a weekend party rally in Bavaria. "It couldn't be more dead."
Asked about Seehofer's comments on a trip to Sofia on Monday, Merkel said: "Germany is and will be an open country."
A spokeswoman for the chancellor said there was no dissent between Merkel and Seehofer because the Bavarian leader had been talking specifically about demands to relax rules that place limits on the number of foreign workers coming to Germany.
"There's no doubt that people from different cultures are welcome in Germany," Merkel spokeswoman Sabine Heimbach said.
But Maria Boehmer, who handles integration issues in the cabinet, said she was "shocked" by Seehofer's comments.
"It's not acceptable to put people from another culture under general suspicion. We don't want to ostracise people. That runs counter to our integration efforts," said Boehmer.
The tone towards foreigners in Germany has shifted recently following the popularity of Sarrazin's book "Deutschland schafft sich ab" (Germany does away with itself). He wrote that Muslim immigrants were lowering the intelligence of German society.
Sarrazin was censured by Merkel and others, but some have since quietly been articulating similar anti-immigrant views.
Conservatives were upset when President Christian Wulff, a moderate Christian Democrat nominated by Merkel, said last week that Islam had its place in Germany alongside Christianity and Judaism.
Claudia Roth, leader of the opposition Greens party, accused Seehofer of making "right-wing populist inflammatory comments". She added: "In essence he's de-naturalising millions of people."
The third partner in Merkel's coalition, the liberal Free Democrats, who often bicker with the CSU, distanced themselves from the Bavarian premier's remarks.
"Seehofer's comments have less to do with the situation on the labour market and more to do with the CSU's standing in opinion polls," said FDP deputy leader Christian Lindner.
(EurActiv with Reuters.)