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."
He has already been fined an undisclosed amount by his club with German media putting that figure between 50,000 and 80,000 euros.
Later on Tuesday, the Hamburg state prosecutors office said they were also investigating the incident for "suspected dangerous bodily harm".
The Peruvian striker has since apologised for his behaviour.
"I blacked out," he told reporters on Monday. "I am very sorry and hope to have the chance to meet the spectator and apologise."
Hamburg, in the running for a Champions League spot earlier this season, are in danger of losing out on European football completely after winning only two of their last 11 league games.
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