The letters included demands for the closure of the Ramstein air force base and the withdrawal of German planes from Syria.
It is not usual practice for the Islamic State to make demands or negotiate in this manner, Frauke Koehler, the state prosecutor said.
He also confirmed that he regarded the media reports as accurate.
One theory is that the devices were planted by somebody from the far right or football hooligans.
Another newspaper, Tagesspiegel, said it had received an email which made racist threats and described the bombing as a warning.
Two people, including Dortmund's Spanish defender, Marc Bartra, needed medical treatment.
Bartra underwent wrist surgery following the bomb and is not expected to play for several weeks.