The talented centre-half, who can also play at right-back, is reported to have suffered lacerations to his hand in the horrific attack.
Bartra, a Spain international with 12 caps, is in his first season with the German club after his summer move from Barcelona.
He swapped the Nou Camp for Westfalenstadion on a four-year deal for a reported fee of eight million euros (£6.8million).
The 26-year-old has been a key player for Dortmund this season, having made 30 appearances.
He played an important role in his side's run to the last eight of the Champions League, featuring in seven of their eight games so far.
A product of Barcelona's famed youth set-up, he made his debut for the Spanish giants in 2011 aged 20.
Borussia Dortmund defender Marc Bartra is in hospital following the attack
Live images from the Borussia Dortmund attack
Tue, April 11, 2017
A football player has been injured after three bombs exploded near Borussia Dortmund's team bus ahead of a Champions League match against Monaco
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A view on the damaged windows of the Borussia Dortmund's team bus after it was hit by three explosions in Dortmund, Germany
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He was never a regular, though, managing only 59 starts in the next five years.
He is perhaps best known to some for being the defender Gareth Bale out-ran for a memorable goal in the 2014 Copa del Rey final.
Bartra has been dating journalist Melissa Jimenez since 2014, and the couple have one child together.
The Spanish international is in his first season with the German club
Hans-Joachim Watzke, Dortmund's chief executive, said: "Bartra was injured, on his hand and his arm, but nothing that would be life-threatening."
Dortmund goalkeeper Roman Burki added: "I was sat in the back row next to Marc Bartra, who was split by the shards of the burst back window.
"After the bang everyone in the bus got their heads down. We didn't know whether there would be more."