Two of the blazes, in which rail cables were set on fire, occurred in western Germany. The third, reported Saturday but which happened Friday, was at Hohenmoelsen in the eastern state of Saxony-Anhalt, the Deutsche Bahn rail company said.
"According to the first elements of the inquiry, this cable fire was also a criminal fire," the company said in a statement. The line was used by goods trains, notable to transport coal.
Deutsche Bahn said it had repaired the line between the western cities of Dusseldorf and Duisburg where the two earlier attacks were reported one kilometre (half a mile) apart on Thursday and Friday.
Five cable sections, each of about 20 metres (65 feet), had to be replaced, the company said.
The first fire on Thursday at a points junction near Dusseldorf caused widespread disruption on one of Germany's busiest rail lines linking its Ruhr industrial region with northern Europe and Switzerland.
Deutsche Bahn said "several hundred" trains had to be cancelled or diverted and tens of thousands of passengers were affected.
A far-left group calling itself the "Angry Birds Kommando" claimed responsibility for the first fire, saying it had acted to stop a "system of destruction" of the environment.
Germany's rail lines have frequently been the target of attacks, with some claimed by radical groups.
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