Spanish defender Marc Bartra suffered injuries in the wrist and arm and underwent an operation Tuesday night.
Ex-Dortmund boss Klopp was in Liverpool with his former colleague Josef Schneck to watch the match when he became aware of the news.
Schneck, the Dortmund press officer during Klopp's time at the club, said: "Jurgen Klopp is just as much affected as all of us".
BVB and AS Monaco chose to postpone the game until Wednesday.
"But first we must look at what is going on before further rumours are spread".
A window of Dortmund's team bus is damaged after an explosion before the Champions League quarterfinal soccer match between Borussia Dortmund and AS Monaco in Dortmund, western Germany, Tuesday, April 11, 2017.
Investigators were checking the authenticity of a letter claiming responsibility that they found near the scene, and were refusing to give any details of its contents, citing the ongoing probe. Players ducked for cover, wondering whether there would be more explosions.
"The team and coaches were shocked".
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The club said other players were safe and there was no danger inside the Signal Iduna Park stadium. "You can imagine yourself whether they slept well or badly", he said.
Bild said police were looking for a vehicle that had been registered overseas. Players and police were preparing to go ahead with the rescheduled match on Wednesday evening, with heavy security in place.
"We are doing everything possible to ensure that the game is played safely", Dortmund's police chief said.
The president of European soccer governing body UEFA, Aleksander Ceferin, said he was "deeply disturbed by the explosions" and that the teams had made the correct call by postponing their match.
Germany has seen matches postponed over security concerns before.
Borussia Dortmund and Monaco supporters showed solitary after explosions rocked football and the world. He wished Bartra a "speedy recovery" and condemned the explosions.
It came days after devices were detonated outside the Stade de France in Paris as France was playing Germany as part of a coordinated attack on the French capital.
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