The officer suffered serious injuries to a hand and an eye, city police chief Alberto Initmi told RaiNews24 television.
Police called in an explosives team after a patrol spotted a suspicious package outside the bookshop, which has ties to a far-right group called Casa Pound.
As the experts approached the package, the blast occurred, said investigators cited by the Italian news agency AGI. The device had been fitted with a timer, they added.
Casa Pound first emerged in Rome in 2003. The movement now has several hundred members, who stage protests against the European Union (EU) and immigration.