Borussia Dortmund's team bus was damaged and a player was injured following three explosions near the vehicle while it was on its way to Tuesday's Champions League game at home to AS Monaco, police said.
The match, a quarter-final first leg, was called off and rescheduled for Wednesday.
Mass-selling German newspaper Bild reported in its online edition that explosive devices were placed in a bush by the road along which the bus was travelling.
"The explosive devices were placed outside the bus. Several windows were broken," police spokesman Gunnar Wortmann was quoted as saying.
In a statement, Dortmund police said earlier that they could not say "exactly what the explosion was or exactly where something exploded".
"According to what is currently known, the windows of the bus were (entirely or partly) smashed and one person was injured," Dortmund police said, adding that the incident happened in Hoechsten, located outside the city.
Dortmund said defender and Spain international Marc Bartra had been taken to hospital.
Bartra, 26, joined Dortmund for eight million euros ($8.48 million) last year from Barcelona, after coming through the Catalan club's youth system. He has made 12 appearances for the Spanish national team.
Borussia Dortmund's managing director Hans-Joachim Watzke was quoted telling Sky TV: "The whole team is in a state of shock."
Police added: "Currently there is no evidence of a threat to the visitors at the stadium."
AS Monaco goalkeeper Danijel Subasic told Croatian daily newspaper 24sata: "We are currently in the stadium, in a safe place, but the feeling's horrible."
Borussia Dortmund said in a statement that there was an "incident" shortly after the departure of team bus from the hotel to the stadium.
"The bus has been damaged in two places," Dortmund said. "One person has been injured and is in the hospital."
Dortmund and UEFA later said that the match would go ahead on Wednesday at 1645 GMT