At around 7:15 pm (1715 GMT) three explosions detonated just minutes after Dortmund's team bus left the squad's hotel.
Here is what we know:
At around 7:15 pm (1715 GMT) three explosions detonated just minutes after Dortmund's team bus left the squad's hotel and headed for their quarter-final, first-leg, tie against Monaco.
The blast shattered the bus windows and left Spanish international Marc Bartra, 26, facing surgery on a broken wrist after he was hit by flying glass.
"The whole team is in a state of shock, you can't get pictures like that out of your head," Dortmund CEO Hans-Joachim Watzke said.
The match was postponed until Wednesday evening.
The state prosecutor's office has opened an investigation into "attempted murder", but police have held off from saying the explosions amounted to an organised terror attack.
"We are assuming that they were a targeted attack against the Dortmund team," said the western German city's police chief Gregor Lange.
German authorities do not at this stage have evidence that the attack was linked to terrorism, German media cited sources close to the security services as saying.
The explosives appear to have been hidden in a hedge and were set off as the bus passed. Investigators believe the bombs may have been homemade using sections of pipes, according to the German daily Bild.
Local prosecutors also revealed that a letter was found close to the site of the blasts. "The letter claims responsibility for what happened," prosecutor Sandra Luecke told journalists. "Its authenticity is being verified," she added, without giving further details on its contents.
Bild said police were looking for a vehicle that had been registered overseas.
Dortmund police said security would be tightened at Wednesday's match, with a major deployment of officers ahead of the kick-off at 6:45 pm.
"We are doing everything possible to ensure that the game is played safely," Dortmund's police chief said.