Bartra was the only person hurt in the incident, which happened as the coach left the team hotel ahead of Tuesday's quarter-final first leg.
Police were unable to specify what type of explosives were used, but they described the devices as "serious", suggesting they had been hidden under a hedge next to a car park.
The match was subsequently postponed and re-arranged for Wednesday, with Dortmund holding a training session ahead of the game.
Borussia Dortmund (@BVB) April 12, 2017
Dortmund had confirmed Bartra would undergo an operation on his broken wrist and club president Reinhard Rauball provided a positive update.
"We have heard that everything went well," he told n-tv.
Meanwhile, Dortmund CEO Hans-Joachim Watzke visited the team prior to their training session and issued a rallying cry to everyone associated with the club.
"I have just told the team in the dressing room to show society that we will not bow to terror," Watzke told the club's website.
"The BVB family was particularly strong when it had to cope with difficult situations.
"This is perhaps the most difficult situation we have had in the past decades and I am sure that we will show ourselves as BVB as strong and united as never before.
"We do not just play for us. We play for everyone. No matter whether Borussian, Bavarian or Schalke.
"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!
"We ask all BVB fans to support our team with full energy for 90 minutes."
The local police force – Polizei Nordrhein-Westfalen Dortmund – confirmed on Wednesday that the federal prosecutor's office for Germany has taken over the investigation.
The office will hold a media conference at 14:00 CET to provide an update on the case.
Messages of support have flooded in from across the world of football, including from former Dortmund player Henrikh Mkhitaryan, now at Manchester United, who tweeted the club his best wishes on Wednesday.
Mkhitaryan made 140 appearances for the German club over three seasons before joining Manchester United last summer.