Ust-Luga is located just a few kilometers from Russia's border with Estonia and across the bay from Finland.
The port is a hub for Russian fossil fuel exports. Governor Aleksandr Drozdenko did not say which part of the port had been hit.
On Monday, Ukraine attacked the port of Primorsk, also in the Gulf of Finland.
According to Russia, up to 400 Ukrainian drones were intercepted overnight on Wednesday. In Belgorod, near the border with Ukraine, Governor Vyacheslav Gladkov said a Ukrainian missile attack caused serious damage to electricity and water facilities.
According to Ukraine, Russia sent nearly 1,000 drones toward Ukraine during the day on Tuesday.
