A letter left near the scene of the attack claimed the atrocity was carried out in retaliation for German military reconnaissance missions against so-called Islamic State in Syria.
And it explicitly mentioned previous ISIS attacks on Europe – including the Berlin Christmas market attack.
One player was injure din the blast on the Borussia Dortmund bus
But a German newspaper has suggested the letter could merely be a deliberate attempt to mislead investigators.
And recent media reports have since suggested police are also examining a second letter of responsibility from the "anti-fascist scene", Focus online magazine said on Wednesday.
The match has been postponed until tonight
ANTIFA, the left wing anti-Nazi group, reportedly claimed responsibility on the internet on Wednesday morning.
In a post online, it says the bus was targetted because the Dortmund team had not done enough to fight racism, right-wing populism and neo-Nazism.
And they added the attack was a "symbol of the politics" of the club.
Borussia Dortmund has been recently plagued with violent, far-right hooliganism – with a recent crackdown leading to stadium bans, resulting in death threats in February for one manager.
Live images from the Borussia Dortmund attack
Tue, April 11, 2017
A football player has been injured after three bombs exploded near Borussia Dortmund's team bus ahead of a Champions League match against Monaco
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A view on the damaged windows of the Borussia Dortmund's team bus after it was hit by three explosions in Dortmund, Germany
However Germany's Sueddeutsche Zeitung newspape suggested a letter found near the scene claimed responsibility for Islamic State
The note allegedly begins "In the name of Allah, the gracious, the merciful" before condeming German Tornado plane flights over Syria.
It claimed because of the Syrian mission sportsmen and other celebrities "in Germany and other Crusading nations" were "on a death list of the Islamic State."
And the letter demanded a withdrawal of the Bundeswehr Tornadoes from Syria as well as the closure of the American air base in Ramstein in Germany.
The Federal Public Prosecutor said in a statement it had taken over the investigation
Player Marc Bartra was injured in the blast
Public prosecutor Sandra Lucke confirmed a note claiming responsibility for the incident was found near the site of the explosions.
She said: "The background [of the attack] is being investigated thoroughly. The investigations are based on a suspicion of [attempted] homicide.
"A claim of responsibility was found near the crime scene. The authenticity is currently being attested.
"I can't tell you more about the content because of ongoing investigations. We are investigating in all directions."
The blast shattered the bus windows
After the bang, we all ducked in the bus and those who could threw themselves to the ground. We did not know had happened.
Goalkeeper Roman Burki
The Federal Public Prosecutor said in a statement it had taken over the investigation and would hold a news conference at midday today.
Polcie also confirmed an explosive-like item was found at the team's hotel after the blasts but it did not ignite.
Player Marc Bartra underwent an operation after breaking a bone in his wrist, but no other players were hurt in the blast.
Goalkeeper Roman Burki, who was sitting at the back of the team bus alongside Bartra, recalled how events unfolded.
Dortmund player Marc Bartra underwent an operation after breaking a bone in his wrist
He said: "We left the hotel at 7:15pm and went down the street. The bus turned down the main street, and there was a giant explosion.
"I was sitting in the back row next to Marc Bartra, who was hit by fragments of the broken glass.
"After the bang, we all ducked in the bus and those who could threw themselves to the ground. We did not know had happened.
"The police were quick on the scene, and we were safe. We're all shocked – nobody thought of a football match in this moment."
The Champions League fixture was postponed after the attack
Tuesday's Champions League quarter-final first leg has now been postponed, and has been rescheduled for Wednesday, with a 5.45pm kick off.
Chief executive Hans-Joachim Watzke said: "In such a crisis situation, all of Borussia will pull together.
"The team and coaches were shocked. Now we must channel it in some way."
There have been a number of previous attacks involving football teams
The bomb was believed to be in a nearby hedge
There have been a number of previous incidents involving football teams and their buses.
In 2010, three died when Angolan rebels attacked the Togo national team bus with machine guns ahead of the African Nations Cup.
In 2015, a bus carrying Fenerbahce players was shot at in northern Turkey.
And last September, six armed men robbed a bus carrying Venezuelan first division club Trujillanos.