The Russian embassy in Panama said on Friday night that the ship would "pass through the Panama canal during the night from the Atlantic Ocean to the Pacific Ocean and back again."
The Panama Canal Authority said the ship entered the canal at 9:00 p.m. local time on Friday (02:00 GMT on Saturday).
The embassy said the trip through the 50-mile (80-km) canal, which was shut to Soviet vessels during the Cold War, "raises the international standing of Panama as a maritime power, and demonstrates to the whole world that the Panama Canal really is a neutral waterway."
Panamanian Foreign Minister Samuel Lewis told reporters: "Here there is no other message than that the canal is open to all of the world's ships."
Captain 1st rank Igor Dygalo, an aide to the Russian Navy commander, told RIA Novosti on Friday that the Admiral Chabanenko would be docked at the Rodman Naval Station from December 6 to 11. Rodman was previously the main naval base for U.S. operations in South America.
The U.S. has not voiced any objections to the ship's presence in the Panama Canal.
On Friday, Dygalo also announced that a Russian task force from the Northern Fleet led by the Admiral Kuznetsov aircraft carrier had begun a tour of duty in the Atlantic and the Mediterranean.
Russia announced last year that its Navy had resumed and would build up a constant presence throughout the world's oceans.
A task force from Russia's Pacific Fleet will leave its main base in Vladivostok on December 9 to take part in joint naval drills with the Indian navy in the Indian Ocean.