A letter found near the bombed Borussia Dortmund team bus "takes responsibility for the act", a German prosecutor says.
Police have also confirmed additional "suspicious objects" were found at the Dortmund team hotel and a letter found near the blast scene in the wake of the bus bombing.
Officers did not reveal the nature of the finds but confirmed that a drone was deployed to assist in the search around the hotel, the Mirror reports .
It was revealed that after the explosions Dortmund players were transferred to the ground in minibuses and later made their way home on private cars.
Gunnar Wortmann, a police spokesman, said: "We will be working throughout the night to discover who was behind this attack. All police and vehicles in Dortmund have been mobilized.
"Three explosions detonating at the exact moment the bus passed by suggest a sophisticated expertise in both bomb building and detonation - perhaps using a mobile phone or a garage door-opening device.
But nearly three hours after the attack there were no real clues as to who may have been behind it.
Neither club has a radical fan following, leading to speculation it may yet be claimed by radical Islamists.
Dortmund goalkeeper Roman Buerki was sitting next to defender Marc Bartra when the bus was hit.
He said: "After the bang we all ducked, and those of us who could dived to the ground. We didn't know if anything else was going to happen.
FIFA president Gianni Infantino released a statement condemning the incident and joined clubs and players around the world in solidarity.
“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," it said.
"We are closely monitoring the condition of BVB’s Marc Bartra, and wish him a speedy recovery from his injuries.
"FIFA condemn the incidents in Dortmund. We are all awaiting further details of the incident."
Heavy security will be in place for the rescheduled Champion League match on Wednesday.
The blasts injured Dortmund player Marc Bartra and came as the team bus set off for the match against Monaco.
"We had to assume, and assumed right from the start, that this was a targeted attack against the team of Borussia Dortmund," said Dortmund Police Chief Gregor Lange.
Investigators are not excluding any possible angles in their investigation, while the "concrete background" to the blasts remains unclear, he said.
He said the authorities will put heavy security in place for Wednesday's match.
"We are preparing for a major operation tomorrow, and we will do everything humanly possible to ensure that the match tomorrow can occur safely," he said.
There were three explosions near the Dortmund bus as the team left the L'Arrivee Hotel and Spa on the outskirts of the western city of Dortmund for the stadium, around six miles away, at 7.15pm local time, police said.
Club spokesman Sascha Fligge said Bartra was operated on late Tuesday for a broken bone in his right wrist and to remove "foreign objects" from his arm.
Dortmund goalkeeper Roman Buerki said the team bus had just pulled out of the hotel driveway when an explosion - a "huge bang" - happened and sent glass flying.
Buerki, who is from Switzerland, told Swiss daily Blick that he was sitting in the last row of the bus, next to Bartra.
Bartra was hit by shards from the broken back window, he added. Players ducked for cover, wondering whether there would be more explosions.
"We're all shocked - nobody thought about a football match in the minutes after that," Buerki said.
Inside the packed stadium, Monaco supporters chanted "Dortmund, Dortmund" in sympathy for the German side.
Dortmund residents, for their part, used social media to offer accommodation to stranded Monaco supporters before their rescheduled match in Europe's premier football club competition.
"The team is totally shocked, that's clear. It's our task now to digest this somehow because it's only 24 hours before we have to play. That's our job," Dortmund chief executive Hans-Joachim Watzke said.
Stadium spokesman Norbert Dickel informed fans already inside the venue of the cancellation, saying that "there is no reason for panic here at the stadium".
Uefa president Aleksander Ceferin said he was "deeply disturbed by the explosions" and that the teams had made the correct call by postponing their match.
In November 2015, Germany's international football friendly against the Netherlands in Hannover was cancelled just before kick-off because police feared an explosive device might be detonated at the stadium.
It came days after devices were detonated outside the Stade de France in Paris as France played Germany, as part of a co-ordinated attack on the French capital.