The increasingly unstable country is seeing a surge of fighting between government and opposition forces, much of it in eastern Jonglei state.
At least 280,000 people there have been displaced since December, according to the United Nations.
Eastern Jonglei's Akobo town, held by opposition forces, hosts a United Nations peacekeeping force of around 100.
It also has a hospital, which has seen an influx of wounded, and is supported by NGOs including the International Committee for the Red Cross (ICRC).
In a short statement, South Sudan People's Defence Forces (SSPDF) spokesperson Lul Ruai Koang said the town and surrounding areas were "the next targets for... offensive military operations".
As a result, he said, the army "orders for closure and immediate withdrawal of UNMISS forces from their Temporary Operating Base in Akobo town within 72 hours".
"UN agencies, NGOs and their staff are ordered to leave within the same window," he added.
Civilians should move to either SSPDF-controlled areas or places they believed safer, he said.
The orders are intended "to avoid unnecessary collateral damage", he added.
In a statement to AFP, UNMISS spokesperson Priyanka Chowdhury said the UN had noted the reported orders and was "seeking clarification from relevant authorities regarding these directives".
In January, the army issued a similar order for different parts of Jonglei state, as they sought to push back an offensive by forces allied to the Sudan People's Liberation Army in Opposition (SPLA-IO).
It is the latest development in fighting between factions allied to vice-president Riek Machar and President Salva Kiir, which has alarmed international observers.
The UN expressed alarm over violence in northern Abiemnom, Ruweng Administrative Area, where some 1,000 people sought shelter with nearby UN peacekeepers.