A defence ministry official was quoted by Yonhap news agency as saying the warship was staying about 50km from the supertanker out of concern it could endanger the lives of its crew of five South Koreans and 19 Filipino nationals.
The destroyer can travel much faster than the supertanker and would be able to reach the ship before it reaches any port.
The tanker, which was seized on Sunday, was travelling to the US from Iraq and can carry more than two million barrels of crude oil - the equivalent of more than one day's worth of Iraqi exports.
South Korea's navy said that the destroyer is armed with a Lynx helicopter, 40 ship-to-ship and ship-to-air missiles and artillery.
In addition about 300 sailors and marines, including a 30-member search and inspection team, are aboard the warship.
Somali pirates commonly target one of the world's busiest maritime trade routes, accruing an estimated $60m in ransoms last year.
The frequent hijackings have increased insurance costs, forcing some ships to go around South Africa instead of through the Suez Canal.
But although attacks in the Gulf of Aden and the Indian Ocean are common, it is rare for pirates to successfully seize the kind of massive supertankers that carry most Gulf crude to refiners.
The first successful assault on a very large crude carrier (VLCC) occurred in late 2008 when pirates took control of the Saudi-owned Sirius Star.
Last November another tanker, the Greek-flagged Maran Centaurus, was seized and held for nearly two months until a ransom, believed to be between $5.5m and $7m, was paid.
In all, Somali pirates were held responsible for 217 acts of piracy in 2009, in which 47 vessels were hijacked and 867 crew members taken hostage.