The council unanimously supported the setting up of a special commission to determine the people and organizations that would face financial sanctions, including the freezing of bank accounts.
The resolution also confirms an embargo on weapons deliveries to Somalia.
A Russian analyst expressed doubts however over the wisdom of the Security Council's decision.
"How these sanctions will work in practice is not clear. There are rumors that the pirates may get money transferred to some accounts, but in practically all cases they demand that ransoms be paid on board the ship in cash. How are these sanctions supposed to work here?" Mikhail Voitenko, the chief editor of the Morskoi Byulleten Sovfracht maritime magazine said.
In October, Russia sent the Neustrashimy (Fearless) missile frigate from the Northern Fleet to Somalia's coast to protect Russian vessels in the country's waters. The Russian warship has prevented the seizure of at least two foreign vessels in the area.
NATO and the EU have recently announced plans to increase their naval presence in the Gulf of Aden and will launch on December 8 a joint naval operation, dubbed Atalanta, against piracy off the coast of Somalia. The operation could involve up to 10 warships.
In early June, the UN Security Council passed a resolution permitting countries to enter Somalia's territorial waters to combat "acts of piracy and armed robbery at sea."
International concern over shipping safety in the region has risen since a huge tanker carrying up to 2 million barrels of Saudi oil was seized on Sunday. Late on Tuesday, an Indian warship opened fire on a pirate vessel, causing it to burst into flames and sink.