A statement from the local police has confirmed the incident occurred as the team set off from their hotel for the first leg of their tie at Signal Iduna Park.
Bartra is reported to be the only player or Dortmund staff member injured in the "bomb attack" and club CEO Hans-Joachim Watzke described the fallout.
"We were shocked, but the team has been shocked the most," he said. "There was a bomb attack when the team left the stadium.
"Marc Bartra is slightly injured, he is in the hospital and it hit his hand."
The police agency had already stated: "We can confirm that there have been three explosions in the area of the team bus.
"In the run-up to the Champions League match of BVB against Monaco, there was an explosion near the BVB team team bus shortly after 19:00 local time.
"To our knowledge the windows of the bus are cracked - fully or partly - and one person was injured.
"It is not yet possible to say exactly what the explosion was or exactly where it exploded."
Meanwhile, the club have also confirmed that the game has been postponed and will instead go ahead on Wednesday.
“Following tonight’s incident involving the Borussia Dortmund team bus," UEFA stated, "the Champions League match between Borussia Dortmund and Monaco has been postponed until tomorrow [17:45 UK time].
"This decision was made after a meeting held at the Westfalenstadion between UEFA, representatives of the two clubs and local authorities.”
Monaco goalkeeper Danijel Subasic commented on the "terrible" feeling in Dortmund, with uncertainty over the cause and reason for the team bus incident.
"We are in the stadium, in a safe, but the feeling is terrible," he told 24sata. "Rather than run out before the full stadium and play in Champions League match, we sit quietly in the locker room and think about where all of this leads.
"I do not know whether and when at all matches to play, but it is currently less important. I hope that Bartra, or anyone that was hurt, will be ok.