Kim Jong-un was in the government meeting and was infuriated after Kim Yong-Jin sat in his chair "with a bad attitude". Another South Korean official said the minister's poor posture was spotted at a meeting on June 29.
"He was later accused of being anti-revolutionary following a probe and a firing squad execution was carried out in July," the official told South Korean newspaper JoongAng Daily.
Two other senior North Korean officials were also banished to "ideological re-education" farms.
Last year it was reported defence minister Hyon Yong-chol was executed by anti-aircraft gun. But the new report corrects claims made in the South Korean media that two other North Korean officials met a similar fate.
Kim Jong-un's regime is especially paranoid in recent weeks after a senior official at the London embassy defected to South Korea with his family.
North Korea rarely announces purges or executions, although state media confirmed the killing of the tyrant's uncle Jang Song Thaek in 2012 for "crimes damaging to the economy".
A former defence minister, Hyun Yong Chol, is also believed to have been executed last year for treason, according to the South's spy agency.
