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.
Three explosive devices went off in a hedge alongside the team bus on April 11, 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 policeman on a motorcycle escorting the bus suffered trauma from the noise of the blast.
"The accused is suspected of having carried out the attack on the team bus of Borussia Dortmund on April 11," prosecutors said after the elite GSG 9 police unit arrested him around dawn in Tuebingen, south of Stuttgart in the state of Baden-Wurttemberg.
"He is charged with attempted murder, setting off explosions and causing serious physical injury," they said in a statement.
He was staying in the same hotel as the team, with a view of the attack scene, and had bought so-called put options on the team's shares on the day of the attack, they said.
These 15,000 options could have been sold at a pre-determined price by June 17, 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.
Sergej. W had allegedly taken out a loan on April 3 to pay for the put options and bought them online from the IP address of the Hotel L'Arrivee, where the team would be staying.
He had reserved the room in mid-March for the periods April 9-13 and 16-20 – 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 euros ($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 euros on Thursday.
The three explosives, packed with metal pieces, were hidden along a 12-metre (40-foot) stretch of the hedge – the first and last devices at ground level, while the one in the middle was placed at a height of about one metre, prosecutors said.
The explosives were remotely triggered, and some metal rods were found as far as 250 metres away.
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 had voiced "considerable doubts" about their authenticity, they said.
An Iraqi man was taken into custody over a suspected Islamist link, but was cleared of involvement in the attack.
Similarly, a purported claim of responsibility 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".
Federal prosecutors scheduled a press conference for 1030 GMT on the investigation, which has involved several hundred police officers.