Three bombs exploded near the club's team bus last night, ahead of a key Champions League match against Monaco.
Defender Marc Bartra was rushed to hospital after picking up injuries in the blast, which took place at around 6:15 BST.
The side's hotel later went into lockdown, according to German newspaper Die Welt.
Officers searched the area using drones amid fears of a further attack on the side.
Football governing body UEFA called off the quarter-final tie, which will instead kick-off at 5:45pm GMT tonight.
Yesterday's other match, between Bartra's former club Barcelona and Juventus, went ahead despite the security scare.
Three bombs exploded near Borussia Dortmund's team bus earlier tonight
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
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An armed police officer speaks to Dortmund player Nuri Sahin
Our task is to process this experience – that's our job
Hans-Joachim Watzke, Dortmund's chief executive, said the explosive devices were hidden behind a hedge.
He said last night: "Bartra was injured, on his hand and his arm, but nothing that would be life-threatening.
"The team is in complete shock. Our task is to process this experience, because the match is taking place in less than 24 hours. That's our job."
Dortmund's chief executive said the bombs were hidden behind a hedge
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Dortmund goalkeeper Roman Burki said: "I was sat in the back row next to Marc Bartra, who was split by the shards of the burst back window.
"After the bang everyone in the bus got their heads down. We didn't know whether there would be more.
"The police arrived quickly, sealed everything off. We are all in shock."