Police said in a statement they were working on the assumption that the blasts ahead of the team's match against Monaco were caused by "serious explosive devices," which may have been hidden in a hedge near a car park.
They didn't elaborate on the possible nature of the devices or say who might have planted them ahead of the first-leg match between Borussia Dortmund and Monaco, which was subsequently called off and rescheduled for Wednesday.
Police said that there were three explosions near the Dortmund team bus as they left their hotel on the outskirts of the western city of Dortmund for the stadium, around 10 kilometers (6 miles) away, at around 7 p.m. local time (1700 GMT).
A window on the bus was damaged and Spanish defender Marc Bartra was injured.
Dortmund said Bartra was taken to a hospital. Dortmund chief executive Hans-Joachim Watzke said Bartra was injured in the arm and hand "but nothing life-threatening."
Dortmund goalkeeper Roman Buerki said the team bus had just pulled out of the hotel driveway when an explosion — a "huge bang" — happened and sent glass flying. The Switzerland international told Swiss daily Blick that he was sitting in the last row of the bus, next to Bartra.
Bartra was hit by shards from the broken back window, he added. Players ducked for cover, wondering whether there would be more explosions.
"We're all shocked — nobody thought about a football match in the minutes after that," he said.
Inside the packed stadium, supporters of Monaco, which plays in the French league, chanted "Dortmund, Dortmund" in sympathy for the German side. Dortmund residents, for their part, used social media to offer accommodation to stranded Monaco supporters ahead of their rescheduled match in Europe's premier soccer club competition.
"The team is totally shocked, that's clear. It's our task now to digest this somehow because it's only 24 hours before we have to play. That's our job," Watzke said.
He added that there was "no alternative" to rescheduling the match for Wednesday, as Monaco also has to play at the weekend and the return Champions League match is scheduled for next week.
"It's a very unfortunate situation but there was no other way," he said.
Stadium spokesman Norbert Dickel informed fans of the cancellation, saying that "there is no reason for panic here at the stadium."
Dortmund recommended that fans stay in the stadium and remain calm to facilitate an "orderly departure." Police say that "nearly all" people in the stadium have left, with no problems.
German Justice Minister Heiko Maas wrote on Twitter: "Shocking news. Our thoughts are with (Borussia Dortmund). You'll never walk alone!"
Germany has seen matches postponed over security concerns before.
In Hannover, in November 2015, Germany's international soccer friendly against the Netherlands was canceled just before kickoff after police feared an explosive device might be detonated at the stadium.
It came days after devices were detonated outside the Stade de France in Paris as France was playing Germany as part of a coordinated attack on the French capital.