The food bank in Essen announced last month it would only register new users if they prove they've got German citizenship, saying some elderly people and women were being scared away.
The chairman of city's integration council, Miguel Martin Gonzalez Kliefken, warned the decision would play into the hands of far-right groups.
In an interview with broadcaster n-tv, Kliefken said the food bank should remove any troublemakers rather than punish people based on their nationality.
The Essen food bank said about three-quarters of its users are foreigners now. Its chairman, Joerg Sartor, told the regional daily WAZ that its staff was concerned about a "lack of respect toward women" among some young foreign men.
Other food banks and migrant rights group rejected the move, saying the problem could be dealt with differently.
"There are no first- or second-class people in need," Berlin's food bank said.
Ulrike Demmer, a spokeswoman for the German government, declined to comment on the specific case but said "Germany is a country of humanity and everyone in need should receive help,"
Despite having a strong social safety net, Germany has about 930 food banks that provide basic goods to people who depend on state benefits.
Copyright 2018 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.