The paper said a further explosion could not be ruled out, Reuters reported.
The Augsburger Allgemeine newspaper said the explosion occurred at the offices of the German Red Cross around 0500 GMT on Friday, adding that police evacuated the area and that five people were injured, but most of them only slightly.
The explosion was probably due to a defect gas line under the street where the building was located, the paper cited police as saying.
Police were not immediately available for comment.