"We currently have a real under-representation of people of immigrant origin in the public service and we have to change that," Merkel said in her weekly podcast.
She added, "When someone has a name that doesn't sound very German, for certain jobs it often happens that they have difficulties in being employed."
Merkel was speaking ahead of an "integration summit" she will chair on Wednesday with 115 representatives of public services and other organisations concerned with integrating immigrants to draw up an action plan.
The government minister concerned with integration, Maria Böhmer, called in January for quotas for civil servants of foreign origin but her plea fell on deaf ears in the regional administrations responsible.
Germany's population of immigrants or their descendants amounts to nearly 20 percent on average, but reaches 26 percent in some regions.
On October 14 Merkel told a meeting of her conservative Christian Democratic Union (CDU) party that "Multikulti", the concept that "we are now living side by side and are happy about it," does not work. "This approach has failed, totally," she said.
Germany has faced an occasionally acrid debate on immigration since August, when a member of the central bank sparked outrage by saying the country was being made "more stupid" by poorly educated and unproductive Muslim migrants.
Thilo Sarrazin has since resigned from the Bundesbank, but his book on the subject
- "Germany Does Itself In" - has flown off the shelves, and polls showed considerable sympathy for some of his views.
Politicians and business leaders meanwhile have said that Germany needs qualified specialists from overseas to keep up the pace of its economic development.