Shoigu is expected to meet President Hassan Rouhani and his counterpart Hossein Dehghan during his trip to discuss the "situation in the region", it said.
The trip comes days after Dehghan visited Moscow on Tuesday, during which Shoigu said Russia and Iran were ready to step up their military cooperation.
Russia and Iran are both longtime allies of Syrian President Bashir al-Assad's regime.
Moscow launched air strikes in support of Syria's government on September 30.
Tehran supports Assad by sending "military advisers" and volunteers to fight alongside the Syrian army.
According to Russian and Iranian media, Iran also wants to buy Sukhoi 30 fighter jets from Russia.