The rocket, which lifted off at 07:38:55 am (GMT 22:38:55 Thursday) from Tongchang-ri in the northwestern county of Cholsan, exploded at 07:41:10, several tens of kilometres south of the launch pad, it said.
"We believe the missile splintered into two parts, probably due to a blast," ministry spokesman Kim Min-Seok told reporters.
"The test is deemed to have failed," he said.
The rocket apparently exploded when it reached an altitude of 70.5 kilometres (43.8 miles) above the sea and was travelling at 5.6 times the speed of sound.
After the explosion, the two chunks of debris continued flying up southward, reaching as high as 151.4 km and passing over South Korea's Baengnyeong island near the sea border.
One of the two chunks further disintegrated into some 10 pieces at 22:47:42 GMT and fell over an wide area in the sea off the South's Taean peninsula.
The other chunk flew further south before breaking up into three pieces and landed in the sea off the southwestern port of Kunsan, the ministry said.
South Korea's navy launched a search to salvage the deris in the Yellow Sea, Kim said, adding it would take "quite a lot of time" to find it, Yonhap news agency reported.
Yonhap said more than a dozen South Korean navy ships, many of them equipped with sonar and backed by divers, were combing the area.
"We believe some large chunks are lying on the sea bed," the spokesman said.
The depth of the sea is between 70 and 100 metres (230 and 330 feet) making it feasible to retrieve large chunks of debris.
"We are aware that there are warships from China, Russia and the United
States around the area (seeking the debris)," he said.
North Korea has said the rocket would place a satellite in orbit for peaceful research purposes, but Western critics and Seoul said the launch was a thinly veiled ballistic missile test, banned by United Nations resolutions.
"It was clearly a ballistic missile test," Major General Shin Won-Sik told reporters.
About four hours after the botched launch, Pyongyang made a rare admission that it had failed, saying its scientists were looking into the cause of the failure.
Copyright AFP (Agence France-Presse), 2012