"The investigation is at this time is for attempted manslaughter. A letter was found near the scene of the crime. The authenticity of the letter is being examined," she said.
Terrorism expert Davis Lewin told Bild that the explosive devices appeared to have been "quite weak".
"That doesn't really fit in with the strategy of Islamist attacks, which until now have gone for large numbers of victims such as in the (truck) attacks in Nice and Berlin," he said.
"On the other hand, terror organizations like ISIS have called upon their followers to go out with home-made bombs. It wouldn't be the first time that something didn't work out the way it was planned. It's just too early to tell what's behind this attack," he added.
A spokesman for Borussia Dortmund said the injured player, Bartra, was being operated on for a broken bone in his right wrist and shrapnel in his arm.
"The bus turned into the main street, when there was a huge boom, a real explosion," Sky television quoted Dortmund goalkeeper Roman Buerki as saying.
"I was sitting in the back row next to Marc Bartra, hit by fragments... after the bang, we all ducked."
Bartra (26), joined Dortmund for 8 million euros ($8.5 million) last year from Barcelona, after coming through the Catalan club's youth system. He has made 12 appearances for the Spanish national team.
"The whole team is in a state of shock," Borussia Dortmund's managing director Hans-Joachim Watzke said.
The stadium emptied quickly and without incident.
"We are currently in the stadium, in a safe place, but the feeling's horrible," AS Monaco goalkeeper Danijel Subasic told.
Dortmund and UEFA said the match would go ahead on Wednesday at 1645 GMT (1245 ET).
"I was deeply disturbed by the explosions which occurred tonight in Dortmund," UEFA President Aleksander Ceferin said.
“The thoughts of every one of us at FIFA are with the people of Dortmund, and the fans of both Borussia Dortmund and Monaco following today’s troubling events," FIFA President Gianni Infantino said.