Essener Tafel, a charity that serves free meals to the poor, had come under fire after it said it would now require new customers to produce German identity papers as a huge migrant influx was displacing locals in need.
In an interview late Monday with RTL television, Merkel said: "One should not make such categorisations. That is not good."
At the same time, the German leader acknowledged that the incident demonstrates the pressure that the volunteers are coming under.
Essener Tafel said last week it had taken the step in order to avoid friction between needy locals and foreigners that could harm acceptance of the newcomers.
Vandals at the weekend sprayed the word "Nazis" on the charity's building and vans, an act police believe was in response to the food bank's migrant halt.