The Federal Criminal Police Office said the 25-year-old, who had no previous police record, was arrested in Cologne on Tuesday after e-mailing anonymous tips about planned attacks to authorities.
But the government quickly ruled out the possibility of a terrorist attack and said the public was never in danger.
"This incident has no links to terrorist or Islamist organizations," a spokesman for the interior ministry said. The suspect appears to be a criminal who acted alone, he added.
The spokesman declined to be named in line with government policy.
Officials found the three alleged explosive devices near Borussia Dortmund's football stadium after questioning the man, the office said. They found another three such objects in his apartment, along with a laptop, chemicals and documents.
Tests have yet to determine whether the devices contained functioning explosives.
The soccer club said the devices were found in a parking lot a few hundred meters (yards) from the stadium.
The suspect had initiated e-mail contact with the German Embassy in Pakistan's capital, Islamabad in February, "with the intention of delivering information" on two allegedly planned attacks in Germany, a statement from the police office said.
Officials determined early in the investigation that the attack scenarios appeared to be fabricated and "may have been the point of departure for a blackmail attempt," it added.
A linguistic analysis of the e-mails suggested a likely link to a so-far unresolved blackmail case involving an unidentified company last year, the police office said.
The man, whose name wasn't released, was arrested at a hotel in Cologne on Tuesday and acknowledged being the anonymous tipster.
The suspect had mentioned a supposedly planned attack near the Dortmund stadium in his e-mails. He told police that he had "made up" details of the planned attacks - but had placed the devices near the stadium and had another three in his apartment. The police office said his motive was unclear.
Borussia Dortmund currently leads German football's top division, the Bundesliga.
The club said its home match Saturday against third-placed Hannover will go ahead, as there is no danger to spectators, but it will beef up security measures at the stadium.