Merkel said she was appalled by Tuesday evening's incident, in which three explosions went off as the Borussia Dortmund bus made its way to a match.
Spanish defender Marc Bartra suffered injuries to his arm and wrist. The attack forced a 24-hour postponement of the team's high-profile clash with AS Monaco. Officials said security had been stepped up for the rescheduled match on Wednesday night, and for a second Champions League quarter-final between Bayern Munich and Real Madrid.
Ralf Jaeger, interior minister in the state of North Rhine-Westphalia which includes Dortmund, said the investigation was looking "in all directions", and it was unclear if one or several attackers were involved.
A spokeswoman for the Federal Prosecutor's Office, which handles probes into suspected terrorism, said the explosive devices had contained strips of metal.
Spokeswoman Frauke Koehler said investigators had found three letters near the scene, all with the same content suggesting a possible Islamist motive.
She said the letters referred to the use of Tornado reconnaissance planes in Syria, which Germany has deployed as part of the military campaign against Islamic State, and also called for the closure of the U.S. military base at Ramstein in western Germany.
Investigators had identified two suspects from the "Islamist scene", searched their apartments and detained one man, she said.
The blasts smashed windows on the bus carrying the players to the stadium. Bartra was operated on for a broken bone in his right wrist and shrapnel in his arm, a team spokesman said.
"We all agree that we are dealing with a despicable act," Merkel said at a business event in the western town of Allendorf.
Read the full article on eurosport.co.uk: Germany detains suspect with Islamist background in Dortmund attack probe