Niersbach told the weekly newspaper Jüdische Allgemeine, in an interview to be published on Thursday, that football chiefs agreed that the visit should be made out of respect to victims of the Holocaust rather than as a public spectacle.
No date has yet been fixed for the visit, he added.
The announcement comes after the chairman of the Central Council of Jews in Germany earlier this month called for the national team to visit one of the memorials dedicated to victims of the Holocaust before the championships in Poland and Ukraine.
More than a million Jews were murdered by the Nazis at the Auschwitz-Birkenau camp, which lies 70 kilometres west of Krakow and around 570km from the Germans' base in Gdansk.
The England team, who will be based in Krakow, have said they also will visit Auschwitz to pay their respects.
The German-Jewish body also urged a visit to Babi Yar, near the Ukrainian capital Kiev, which hosts the Euro 2012 final on July 1, where SS soldiers massacred more than 33,000 Jews in late September 1941 during a single operation.
Niersbach said: "I myself have already been to Auschwitz and I know from my own experience how much the memory of the Holocaust is important."
In the interview, Niersbach also touched on the verbal attacks against Kaiserslautern's Israeli striker Itay Shechter earlier this month, saying that, "anti-Semitism is a persistent problem in society and for all of us in football."
The DFB president, however, said he was "impressed by the dignity and restraint with which Itay Shechter handled the situation and how the Kaiserslautern fans supported him."