Spanish international Marc Bartra is reported to have been injured and some of the vehicle's windows were broken.
He was said to have been hit by shards of glass. Other players in the German side are thought to have been unhurt.
The blasts happened as the vehicle was leaving the team hotel in Dortmund ahead of the side's Champions League match tonight.
The explosions took place 10km from the Westfalenstadion stadium, where the team was due to face Monaco in the quarter-finals.
The game has now been postponed until Wednesday.
Borussia Dortmund said there was no danger at the stadium, where around 80,000 people would have been expected tonight.
It is not known what caused the blasts.