The warship had been in the Gulf of Aden on anti-piracy operations and was ordered to move toward the South Korean-operated tanker's expected location in Somali waters nearly 1,000 miles (1,500 kilometers) southeast, South Korea's Foreign Ministry said.
The South Korean destroyer will need a little over a day to catch up to the tanker, ministry spokesman Kim Young-sun said Monday.
"We're doing this in cooperation with the ships of our allies," Kim said, declining further comment citing efforts to "ensure the safety of the crewmen and the success of possible negotiations."
The navy received a call Sunday from the Samho Dream supertanker saying three pirates had boarded, and then there was no more contact, a ministry official said late Sunday. She spoke on condition of anonymity in line with ministry policy.
The vessel operator said Monday it had lost contact with the ship. "We currently cannot reach the Samho Dream's captain," Cho Yong-woo of Busan, South Korea-based Samho Shipping, told The Associated Press. He said the ship is owned by a Singaporean company.
The tanker was sailing from Iraq to the U.S. state of Louisiana with 24 sailors -- 5 South Koreans and 19 Filipinos -- on board, the ministry said.
The Philippines' Department of Foreign Affairs said in a statement that officials were coordinating with the Marshall Island-flagged ship's principal, the local manning agency and the Philippine embassies in Nairobi and Seoul "for the early resolution of the case."
The Samho Dream had no security detail because Somali pirates were believed to be inactive in the area where the tanker was seized, Cho said.
The 300,000-ton-class vessel was about 930 miles (1,500 kilometers) southeast of the Gulf of Aden at the time of the apparent hijacking, according to the Foreign Ministry.
Valero Energy Corp., an oil and gas refining company based in San Antonio, Texas, said it owns the cargo on board the tanker, but could not confirm the hijacking.
"We've had reports to that effect, but there's been no official confirmation," said Bill Day, a spokesman for Valero. But, he added, "Everything points to that."
Since 2006, four South Korean vessels have been hijacked by Somali pirates, with some being held for months, though all were eventually released.
Somalia has not had a functioning government since 1991 and its lawless coastline is a haven for pirates. Multimillion-dollar ransoms have become a way to make money in the impoverished nation.
In one deal involving a hijacked South Korean tuna fishing vessel, eight South Korean hostages were set free along with nine Indonesians, five Vietnamese and three Chinese after a ransom of more than $800,000 was paid to a Somali militant group.
Somalia is located along the Gulf of Aden, which connects the Red Sea and the Indian Ocean and is one of the world's busiest waterways with some 20,000 ships passing through each year.
An international flotilla, including warships from the United States, the European Union, NATO, Japan and China, has been patrolling the area to deal with the attacks that have endangered the vital sea lane that links Asia to Europe.