The Italian news agency ANSA said a police operation targeted the Informal Anarchist Federation and another far-leftist group, the International Revolutionary Front.
Along with the arrests, which police said they were in the process of making, buildings throughout Italy were being searched, police said.
ANSA said those being arrested are suspected in attacks including letter bombs sent last year to Italian tax-collection agency Equitalia, Deutsche Bank in Frankfurt, Germany, and the Greek Embassy in Paris.
The IAF claimed responsibility for a May 7 attack in which Ansaldo Nucleare Chief Executive Officer Roberto Adinolfi was shot in the leg in Genoa. Investigators said none of the 10 people being arrested were suspected of involvement in the shooting.