The investigation is focused on two suspects from the "Islamist spectrum," spokeswoman Frauke Koehler said. Their homes have been searched and one has been temporarily detained, she said.
Three explosive devices shattered windows and injured a player on the Borussia Dortmund team bus Tuesday evening local time as the German squad was en route to its home Champions League match against AS Monaco. The game was postponed to the next day; AS Monaco won 3-2 Wednesday
The devices, which were hidden behind a hedge, contained pieces of metal and had a reach of 100 meters (109 yards), the prosecutor's office said.
Based on the type of detonator and explosive involved, German authorities assume "terrorist involvement" but the motives are unclear, Koehler said.
Letter threatens sporting figures, celebrities
One of two claims of responsibility for the attack -- found in three copies of the same letter left at the scene -- purports to be from an ISIS sympathizer, according to a copy of the document obtained by CNN from a source knowledgeable about the investigation.
The single-page letter, typed in German, calls on Germany to pull its Tornado jets from missions over Syria, calls for the closure of the US Air Force's Ramstein air base in Germany and refers to the "blessed brothers" behind the December 2016 Berlin truck attack
German Tornado jets have been carrying out surveillance over Syria since January 2016, regularly taking photos of potential targets for anti-ISIS coalition airstrikes.
The letter also says that famous sporting figures, actors, singers, and celebrities in Germany and "other Crusader nations" are, from now on, on the "death list of the Islamic State" unless these requirements are fulfilled.
The letter appears to have been written by a non-native German speaker or someone trying to pass themselves off as a non-native German speaker.
A second claim of responsibility, apparently from the far-left, has been circulating online, the prosecutor's office said, but there are doubts about it.
Security tightened for rescheduled match
The match was played Wednesday night amid tight security. Fans could not bring backpacks into Westfalenstadion, the Borussia Dortmund stadium also known as Signal Iduna Park. Twice during the evening, security officials closed entrances and exits at the stadium because of suspicious objects, though both objects were later deemed to be safe.
State interior minister for North Rhine-Westphalia Ralf Jaeger, speaking in Dusseldorf earlier, said the number of police had been increased significantly in Dortmund ahead of the rescheduled game.
Jaeger said the perpetrators likely targeted the team in order to get as much attention as possible and to try to make people feel frightened and unsafe.
He said the German interior minister would attend the match and that "we're keeping our fingers crossed for the team."
Jaeger said investigators were looking into all possible motives. "It could be extreme left, extreme right, someone who is violent, Islamists -- police need time to carry out their investigation," he said.
Chancellor Angela Merkel was "horrified" by the news of the "repugnant" attack, spokesman Steffen Seibert said.
Player undergoes surgery
Spanish defender Marc Bartra, 26, suffered injuries to an arm and hand, the team said. Bartra, who has played 29 games in all competitions for Dortmund this season, was treated at the scene and hospitalized.
The team later said Bartra was in surgery for a broken radius -- a bone in the forearm -- and for "bits of debris lodged in his hand." He did not play Wednesday.
Bartra posted on social media Wednesday afternoon saying he was "doing much better."
Thanks for all your messages! All my strength to my team mates, fans and to @BVB for tonight!" he tweeted, using another name for his team.
Some Germans opened their homes to Monaco supporters who found themselves without a place to stay on Tuesday night after the match was rescheduled.