Roberto Adinolfi was shot in the leg by an assailant wearing a helmet who fled the scene as a passenger on the back of a motor scooter. Adinolfi underwent surgery and was in good condition, Italian media reported.
Genoa's chief prosecutor, Michele Di Lecce, said all motives were being considered, including domestic terrorism.
Adinolfi, 59, is CEO of Ansaldo Nuclear, a division of the state-controlled Finmeccanica company that specializes in nuclear engineering and which has designed plants in China, the Czech Republic and Romania. Adinolfi has been CEO since 2007.
Finmeccanica's CEO Giuseppe Orsi said if terrorism was confirmed, the attack "represents a signal of alarm not to be underestimated" in terms of the economic difficulties brought on by the financial crisis.
He also decried any attempt to use the financial crisis "for ideological ends."