Seven of the 10 victims were Jewish, leading to the theory that the attack on July 27, 2000 had an anti-foreigner or anti-semitic motive.
Among those wounded was a 26-year-old woman who lost her unborn baby.
The 50-year-old suspect was arrested in the town of Ratingen, near the western city of Duesseldorf, police said.
News weekly Der Spiegel said the man was a former soldier known as a notorious neo-Nazi who once ran a military surplus store.
Germany has long been plagued by far-right violence.
In 2011, the country was shocked by revelations that a string of murders blamed on migrant crime gangs were in fact carried out by a neo-Nazi cell.
Known as NSU, short for National Socialist Underground, the cell consisted of a trio of far-right militants who shot dead eight men with Turkish roots, a Greek migrant and a German policewoman between 2000 and 2007.
Violent attacks against migrants have been on the rise again since Chancellor Angela Merkel's controversial decision in 2015 to open the country's borders to those fleeing conflict and persecution.
The pipe bomb attack in 2000 sent shockwaves through Germany.
The device was placed on a busy footbridge leading into the Wehrhahn station of Duesseldorf's S-Bahn urban rail system.
The victims were on their way back from a German language class when they were hit by the blast.
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