The spokesperson said he could not provide further details on the attack, which took place in Illerkirchberg, a town of around 5,000 people west of Munich.
German daily Bild had reported earlier that the attacker had wielded a knife.
After arriving at the scene and tending to the two severely injured girls, police found that a suspect had fled into a neighbouring building, Wolfgang Juergens, spokesperson for police in the German city of Ulm, told local broadcaster SWR.
The people inside the building have been taken into custody, he said, without saying how many people had been found and whether any of them were the suspected attacker, Reuters reported.
"Everything further will come out of the ongoing investigation," he said.
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