FJP offices were set alight in the Mediterranean city of Alexandria and in Aga in the Nile Delta province of Daqahliya, security officials said.
Television footage showed plumes of smoke rising from the building in Alexandria as pro- and anti-Mursi protesters clashed.
The offices in Aga were ransacked and then burned, the officials said.
A Muslim Brotherhood spokesman, Gehad al-Haddad, in a Twitter message accused remnants of ousted president Hosni Mubarak's National Democratic Party of attacking the offices.
The unrest comes ahead of mass protests planned against Mursi on Sunday's first anniversary of his becoming president.
