Guerrero, who only recently returned from a seven-month injury absence, was caught on camera turning and throwing a plastic water bottle at a Hamburg fan while walking off the pitch after a disappointing 0-0 draw against Hanover 96.
"The DFB has initiated an investigation against Paolo Guerrero ... Guerrero is suspected of a violent act against a spectator," the DFB said in a statement on Tuesday.
"Television pictures show him throwing a bottle into the stands and hitting a spectator in the face."
Later on Tuesday, the Hamburg state prosecutors office said they were also investigating the incident for "suspected dangerous bodily harm".
"I blacked out," he told reporters on Monday. "I am very sorry and hope to have the chance to meet the spectator and apologise."
