The letter and a kitchen knife were found by a delivery man last week when he tried to re-pack a torn parcel addressed to Defence Minister Han Min-Koo, the defence ministry said.
"Through our investigation, we are trying to determine whether North Korea has been involved," a ministry spokesman told AFP.
The minister has vowed to take strong action against any provocations by North Korea, which has conducted a series of missile and rocket tests in recent months.
Pyongyang has issued a series of blistering threats against Han, the ministry said.
The letter, sent by the "International Peace Action Corps", threatened to punish Han and his family, condemning the minister for his perceived hardline stance against North Korea, the ministry said, adding the organisation was nonexistent.
It also accused Han of bringing "a fire cloud of a nuclear war to the Korean peninsula".
The ministry said the knife had red letters reading "Han Min-Koo" on one side, and "Execution" on the other side.
UN resolutions bar North Korea from conducting any launches using ballistic missile technology.
But the North has defended the missile launches as a legitimate exercise in self-defence and a response to US war manoeuvres.