The vehicle was damaged as three explosions occurred while the Bundesliga squad were en route from the team hotel to Signal Iduna Park for Tuesday's Champions League quarter-final first leg with Monaco, which was consequently postponed.
Defender Marc Bartra was injured in the incident and has since undergone surgery on his wrist.
Police were unable to specify what type of explosives were used, but they described the devices as "serious" and chief Gregor Lange confirmed they were working under the assumption that it was a "targeted attack on BVB's team".
In response, UEFA has moved to reconsider safety arrangements for the three games taking place on Wednesday, with Atletico Madrid hosting Leicester City, Real Madrid heading to Bayern Munich, and Dortmund welcoming Monaco for their rearranged meeting.
"While there has been no specific intelligence regarding any threat to tonight’s matches, we would like to assure teams, officials and supporters that UEFA always insists upon the highest standards of safety and security arrangements for competition matches, and that the safety of everyone attending UEFA's matches is our highest priority," read a statement from European football's governing body.
"Following last night's incident in Dortmund, UEFA - in co-operation with the police, security services, stadium management and the clubs involved - is reviewing the security arrangements for tonight's matches and security procedures will be enhanced accordingly wherever needed.
"We kindly ask all supporters to allow extra time for the possibility of enhanced security checks."
Dortmund CEO Hans-Joachim Watzke, who visited the team prior to a pre-match training session, issued a message of defiance.
"I have just told the team in the dressing room to show society that we will not bow to terror," he told the club's website.
"We want to show that terror and hatred can never determine our actions. And of course we play for Marc Bartra, who wants to see his team win."