A letter found near the scene of a bomb attack on the Borussia Dortmund team bus claims responsibility for the blasts, according to prosecutors.
Police are investigating three "serious explosive devices" which went off as the players and coaching staff left a hotel ahead of a Champions League match in Germany.
The direction of the probe remains "open", police spokeswoman Nina Vogt told ZDF television.
"Of course our investigations have to go in all directions to begin with."
Defender Marc Bartra, a Spain international, was taken to hospital after being injured by shattered glass from the coach's windows.
He has had an operation for a broken bone in his hand.
Other players were unhurt, but the match against Monaco was postponed.
Club chief executive Hans-Joachim Watzke said "the team are obviously completely shocked" after what police believe was a targeted attack against the football side.
Police said they believe the devices may have been hidden in a hedge near a parking area at the L'Arrivee Hotel and Spa on the outskirts of Dortmund.
Mr Watzke said he understood the blasts were by the hotel exit and happened as the bus was passing.
A letter that "takes responsibility for the act" was found near the coach and its authenticity is being verified, according to prosecutors.
The team's Swiss goalkeeper, Roman Buerki, was sitting in the back row of the bus, next to Bartra.
He said players ducked for cover, wondering if there would be more explosions.
The blasts happened around six miles from the Westfalenstadion, where the team had been due to face the French side in a quarter-final first-leg tie.
The game will now be played on Wednesday evening.
Borussia Dortmund said there was no danger at the stadium, where around 80,000 people would have been expected for the game.
The club thanked Monaco supporters for their "patience and understanding" and for chanting "Dortmund! Dortmund!" when the reason for the postponement was announced.
Mr Watzke said: "It was all very disciplined.
"I think with all the social media we have these days that people pretty much knew what was going on."
Monaco fans were offered a place to stay for the night by Borussia Dortmund supporters on social media after the match was rearranged.
The German club sent out a tweet about the scheme under the hashtag #bedforawayfans.
Fans of both clubs posted pictures of themselves enjoying meals and a drink together.
Monaco also offered their fans €80 each to stay in a hotel for the night.
Borussia Dortmund president Reinhard Rauball said he was confident the team would rise to the occasion when they take to the field again despite the experience.
"How is the team doing? You can imagine yourself whether they slept well or badly," he said.
"This is certainly a difficult situation for the team which, I think, has not experienced such a situation before," said Mr Rauball.
"However, we expect and I am confident that the team will do its best and deliver a spectacle in the Champions League this evening."