They said the man, identified only as 28-year-old Sergej W., was hoping to profit from a drop in the football team's share price as a result of the attack last week.
Three explosive devices went off in a hedge alongside the team bus on April 11th, minutes after it left the squad's hotel heading for a Champions League quarter-final match at home against Monaco.
The blast shattered the bus windows, and Spanish international Marc Bartra, 26, was wounded, forcing him to undergo surgery for a broken wrist.
A motorcycle police officer suffered inner ear damage from the blast.
"The accused is suspected of having carried out the attack on the team bus of Borussia Dortmund on April 11th," prosecutors said after the elite GSG 9 police unit arrested the suspect in Tübingen near Stuttgart in the southwestern state of Baden-Württemberg.
"He is charged with attempted murder, setting off explosions and causing serious physical injury."
The suspect was staying in the same hotel as the team, had a view of the scene where the attack was to be staged and had bought so-called put options on the team's shares on the day of the incident, prosecutors said.
These 15,000 options could have been sold at a pre-determined price by June 17th, with a sharp fall in the share price promising a high profit.
"A significant drop in the price could have been expected if, as a result of the attack, players had been seriously injured or even killed," the prosecutors said.
Packed with metal
Sergej. W had allegedly taken out a loan of tens of thousands of euros to pay for the put options, most of which he purchased online from the IP address of the Hotel L'Arrivee, where the team was staying, prosecutors said.
He had reserved the room in mid-March for the periods April 9th-13th and 16th-20th - coinciding with the team's two scheduled matches against Monaco, though it was not yet clear at the time which one would be held in Dortmund.
He hoped to earn as much as €3.9 million ($4.2 million), the Bild newspaper reported.
The team's share price has fallen by about 5.5 percent on the Deutsche Boerse since the attack and closed at €5.36 on Thursday.
The three explosive devices, packed with metal pieces, were hidden along a 12-metre (40-foot) stretch of the hedge - two of them at ground level, while the third was placed at a height of about one metre, prosecutors said.
The devices were remotely triggered, and shrapnel was found as far as 250 metres away.
Citing unnamed investigators, Bild said police believed the suspect was capable of building a remotely-triggered bomb, having won an educational award in electronics and engineering in 2005.
He had drawn attention at the hotel, reported Bild - first by insisting on a window room facing the front and then, in the pandemonium after the blasts, by calmly walking to its restaurant to order a steak.
Three purported claims of responsibility stating a radical Islamist motive were found at the scene, on paper bearing no fingerprints, prosecutors said.
But Islamic studies scholars voiced "considerable doubts" about their authenticity, they said.
An Iraqi man was taken into custody over a suspected Islamist link but was later cleared of involvement in the attack.
Similarly, a purported claim stating a far-right motive sent to German media bore "contradictions and inconsistencies", prosecutors said, adding that there was "no indication that it was sent by the perpetrator".
Borussia Dortmund thanked police, who had reportedly been surveilling the suspect for days, following leads including a tipoff from a financial sector source.
"We are very grateful and hope that with the suspect's arrest, the perpetrator responsible for the despicable attack against our players and staff members has been caught," the club said in a statement.
The fact that, aside from Bartra, "no others were wounded or even killed, was - as we know today - solely due to huge luck".
Team captain Marcel Schmelzer said the side hoped "we will learn the actual background of the attack" which would help "all those who sat on the bus... come to terms with" the traumatic event.
Interior Minister Thomas de Maiziere labelled the arrest "a great success" and said that, if confirmed, "this would be a particularly repugnant motive".
By Frank Zeller