The decision was announced by Lee Jong-seok, the unification minister, on Thursday.
Lee also said that Seoul would take action against the North beyond a UN Security Council resolution that mandated trade and financial sanctions.
"The government will ban the passage and stay [in the South] of persons and their family designated by [UN Security Council] sanctions committee," Lee told a parliamentary committee.
Lee said Seoul would also invoke a maritime agreement with the North to search North Korean ships that make port calls in the South.
He did not comment on whether Seoul would suspend commercial projects in the North in an industrial zone where South Korean firms operate and a resort is open to foreign tourists.
The comments came a day after the North threatened war if Seoul joined what it called a "criminal act" led by Washington to stifle the North, referring to the resolution.
"The government will ban the passage and stay [in the South] of persons and their family designated by [UN Security Council] sanctions committee"
Lee Jong-seok, South Korean unification minister
North Korea said on Wednesday any action by Seoul under the UN resolution would "drive the inter-Korean relations to a catastrophe" and would be "a grave provocative act of leading the situation on the Korean peninsula to a war crisis".
Seoul has been cautious about taking steps against the North out of concern that it might increase tension on the Korean peninsula and hurt bilateral ties that it has worked for six years to build.
But Seoul has said it would not be business as usual after the nuclear test on October 9, which defied international warnings and led to the Security Council resolution banning trade of goods and transfer of funds that aid the North's weapons programmes.