Dortmund's press spokesman confirmed the 26-year-old Bartra needed an operation on his right wrist.
"Marc Bartra will be operated on, he has broken the radius (bone) in his right wrist and there are foreign bodies in the arm," said Sascha Fligge.
"The Borussia family has shown that we close ranks in difficult times and that's what we also want to do for Marc."
A police spokesman confirmed that Bartra's status had been changed from 'lightly' to 'badly injured'.
Fligge said that with Dortmund scheduled to play Bayer Leverkusen in the Bundesliga on Saturday, before next Wednesday's return leg at Monaco, there was no alternative but to reschedule the first leg for Wednesday.
The Dortmund spokesman also confirmed the team bus had strengthened glass in its windows, but the force of the blasts still shattered several panes.